ring_theory.fractional_ideal ⟷ Mathlib.RingTheory.FractionalIdeal.Operations

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

@@ -710,15 +710,15 @@ protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop}
 instance : NatCast (FractionalIdeal S P) :=
   ⟨Nat.unaryCast⟩
 
-#print FractionalIdeal.coe_nat_cast /-
-theorem coe_nat_cast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
+#print FractionalIdeal.coe_natCast /-
+theorem coe_natCast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
   show ↑n.unaryCast = ↑n by induction n <;> simp [*, Nat.unaryCast]
-#align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_cast
+#align fractional_ideal.coe_nat_cast FractionalIdeal.coe_natCast
 -/
 
 instance : CommSemiring (FractionalIdeal S P) :=
   Function.Injective.commSemiring coe Subtype.coe_injective coe_zero coe_one coe_add coe_mul
-    (fun _ _ => coe_nsmul _ _) coe_pow coe_nat_cast
+    (fun _ _ => coe_nsmul _ _) coe_pow coe_natCast
 
 variable (S P)
 

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

@@ -570,7 +570,7 @@ theorem IsFractional.nsmul {I : Submodule R P} :
     convert ((0 : Ideal R) : FractionalIdeal S P).IsFractional
     simp
   | n + 1, h => by
-    rw [succ_nsmul]
+    rw [succ_nsmul']
     exact h.sup (_root_.is_fractional.nsmul n h)
 #align is_fractional.nsmul IsFractional.nsmul
 -/
@@ -606,7 +606,7 @@ theorem IsFractional.mul {I J : Submodule R P} :
 theorem IsFractional.pow {I : Submodule R P} (h : IsFractional S I) :
     ∀ n : ℕ, IsFractional S (I ^ n : Submodule R P)
   | 0 => isFractional_of_le_one _ (pow_zero _).le
-  | n + 1 => (pow_succ I n).symm ▸ h.mul (_root_.is_fractional.pow n)
+  | n + 1 => (pow_succ' I n).symm ▸ h.mul (_root_.is_fractional.pow n)
 #align is_fractional.pow IsFractional.pow
 -/
 
@@ -1172,7 +1172,7 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 #print FractionalIdeal.exists_ne_zero_mem_isInteger /-
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
@@ -1477,7 +1477,7 @@ theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
     rw [map_div₀, IsFractionRing.mk'_eq_div]
   · rintro ⟨x, rfl⟩
     obtain ⟨y, y_ne, y_mem⟩ := exists_ne_zero_mem_is_integer hI
-    rw [← div_mul_cancel x y_ne, RingHom.map_mul, ← Algebra.smul_def]
+    rw [← div_mul_cancel₀ x y_ne, RingHom.map_mul, ← Algebra.smul_def]
     exact Submodule.smul_mem I _ y_mem
 #align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_one
 -/
@@ -1654,7 +1654,7 @@ theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingle
   by
   induction' n with n hn
   · rw [pow_zero, pow_zero, span_singleton_one]
-  · rw [pow_succ, hn, span_singleton_mul_span_singleton, pow_succ]
+  · rw [pow_succ', hn, span_singleton_mul_span_singleton, pow_succ']
 #align fractional_ideal.span_singleton_pow FractionalIdeal.spanSingleton_pow
 -/
 

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

@@ -702,7 +702,7 @@ theorem coe_pow (I : FractionalIdeal S P) (n : ℕ) : ↑(I ^ n) = (I ^ n : Subm
 protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop} {r : P}
     (hr : r ∈ I * J) (hm : ∀ i ∈ I, ∀ j ∈ J, C (i * j)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
   by
-  simp only [mul_def] at hr 
+  simp only [mul_def] at hr
   exact Submodule.mul_induction_on hr hm ha
 #align fractional_ideal.mul_induction_on FractionalIdeal.mul_induction_on
 -/
@@ -1367,7 +1367,7 @@ theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : Fra
   by_cases hI_nz : I = 0
   · rw [hI_nz, div_zero, MulZeroClass.mul_zero]; exact zero_le 0
   · rw [← coe_le_coe, coe_mul, coe_div hI_nz, coe_one]
-    rw [← coe_le_coe, coe_one] at hI 
+    rw [← coe_le_coe, coe_one] at hI
     exact Submodule.le_self_mul_one_div hI
 #align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_div
 -/
@@ -1776,7 +1776,7 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
   have h_spand : span_singleton R₁⁰ d ≠ 0 := mt span_singleton_eq_zero_iff.mp hd
   apply le_antisymm
   · intro x hx
-    rw [← mem_coe, coe_div h_spand, Submodule.mem_div_iff_forall_mul_mem] at hx 
+    rw [← mem_coe, coe_div h_spand, Submodule.mem_div_iff_forall_mul_mem] at hx
     specialize hx d (mem_span_singleton_self R₁⁰ d)
     have h_xd : x = d⁻¹ * (x * d) := by field_simp
     rw [← mem_coe, coe_mul, one_div_span_singleton, h_xd]
@@ -1801,14 +1801,14 @@ theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
       nonzero, ext fun x => Iff.trans ⟨_, _⟩ mem_singleton_mul.symm⟩
   · intro hx
     obtain ⟨x', hx'⟩ := ha x hx
-    rw [Algebra.smul_def] at hx' 
+    rw [Algebra.smul_def] at hx'
     refine' ⟨algebraMap R₁ K x', (mem_coe_ideal _).mpr ⟨x', mem_singleton_mul.mpr _, rfl⟩, _⟩
     · exact ⟨x, hx, hx'⟩
     · rw [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
   · rintro ⟨y, hy, rfl⟩
     obtain ⟨x', hx', rfl⟩ := (mem_coe_ideal _).mp hy
     obtain ⟨y', hy', hx'⟩ := mem_singleton_mul.mp hx'
-    rw [Algebra.linearMap_apply] at hx' 
+    rw [Algebra.linearMap_apply] at hx'
     rwa [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
 #align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mul
 -/
@@ -1820,7 +1820,7 @@ instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Alg
   obtain ⟨a, aI, -, ha⟩ := exists_eq_span_singleton_mul I
   use(algebraMap R K a)⁻¹ * algebraMap R K (generator aI)
   suffices I = span_singleton R⁰ ((algebraMap R K a)⁻¹ * algebraMap R K (generator aI)) by
-    rw [span_singleton] at this ; exact congr_arg Subtype.val this
+    rw [span_singleton] at this; exact congr_arg Subtype.val this
   conv_lhs => rw [ha, ← span_singleton_generator aI]
   rw [Ideal.submodule_span_eq, coe_ideal_span_singleton (generator aI),
     span_singleton_mul_span_singleton]
@@ -1866,8 +1866,8 @@ attribute [local instance] Classical.propDecidable
 
 #print FractionalIdeal.isNoetherian_zero /-
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
-  isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by
-    rw [coe_zero] at hI ; rw [le_bot_iff.mp hI]; exact fg_bot
+  isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by rw [coe_zero] at hI;
+    rw [le_bot_iff.mp hI]; exact fg_bot
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 -/
 
@@ -1904,7 +1904,7 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
   have h_spanx : span_singleton R₁⁰ (algebraMap R₁ K x) ≠ 0 := span_singleton_ne_zero_iff.mpr h_gx
   rw [is_noetherian_iff] at hI ⊢
   intro J hJ
-  rw [← div_span_singleton, le_div_iff_mul_le h_spanx] at hJ 
+  rw [← div_span_singleton, le_div_iff_mul_le h_spanx] at hJ
   obtain ⟨s, hs⟩ := hI _ hJ
   use s * {(algebraMap R₁ K x)⁻¹}
   rw [Finset.coe_mul, Finset.coe_singleton, ← span_mul_span, hs, ← coe_span_singleton R₁⁰, ←

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

@@ -1931,7 +1931,7 @@ variable {R P} (S) (x : P) (hx : IsIntegral R x)
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Algebra.adjoin R ({x} : Set P)).toSubmodule :=
-  isFractional_of_fg (IsIntegral.fg_adjoin_singleton x hx)
+  isFractional_of_fg (fG_adjoin_singleton_of_integral x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 -/
 

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

@@ -1931,7 +1931,7 @@ variable {R P} (S) (x : P) (hx : IsIntegral R x)
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Algebra.adjoin R ({x} : Set P)).toSubmodule :=
-  isFractional_of_fg (FG_adjoin_singleton_of_integral x hx)
+  isFractional_of_fg (IsIntegral.fg_adjoin_singleton x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 -/
 

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

@@ -1466,7 +1466,7 @@ variable [Algebra R₁ K] [IsFractionRing R₁ K] [Algebra K L] [IsFractionRing
 #print FractionalIdeal.eq_zero_or_one /-
 theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
   by
-  rw [or_iff_not_imp_left]
+  rw [Classical.or_iff_not_imp_left]
   intro hI
   simp_rw [@SetLike.ext_iff _ _ _ I 1, mem_one_iff]
   intro x

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

@@ -3,13 +3,13 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Filippo A. E. Nuccio
 -/
-import Mathbin.Algebra.BigOperators.Finprod
-import Mathbin.RingTheory.IntegralClosure
-import Mathbin.RingTheory.Localization.Integer
-import Mathbin.RingTheory.Localization.Submodule
-import Mathbin.RingTheory.Noetherian
-import Mathbin.RingTheory.PrincipalIdealDomain
-import Mathbin.Tactic.FieldSimp
+import Algebra.BigOperators.Finprod
+import RingTheory.IntegralClosure
+import RingTheory.Localization.Integer
+import RingTheory.Localization.Submodule
+import RingTheory.Noetherian
+import RingTheory.PrincipalIdealDomain
+import Tactic.FieldSimp
 
 #align_import ring_theory.fractional_ideal from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
 
@@ -1172,7 +1172,7 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 #print FractionalIdeal.exists_ne_zero_mem_isInteger /-
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :

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

@@ -484,7 +484,7 @@ theorem eq_zero_iff {I : FractionalIdeal S P} : I = 0 ↔ ∀ x ∈ I, x = (0 :
 theorem IsFractional.sup {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I ⊔ J)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
-    ⟨aI * aJ, S.mul_mem haI haJ, fun b hb =>
+    ⟨aI * aJ, S.hMul_mem haI haJ, fun b hb =>
       by
       rcases mem_sup.mp hb with ⟨bI, hbI, bJ, hbJ, rfl⟩
       rw [smul_add]
@@ -588,7 +588,7 @@ theorem coe_nsmul (n : ℕ) (I : FractionalIdeal S P) : (↑(n • I) : Submodul
 theorem IsFractional.mul {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I * J : Submodule R P)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
-    ⟨aI * aJ, S.mul_mem haI haJ, fun b hb =>
+    ⟨aI * aJ, S.hMul_mem haI haJ, fun b hb =>
       by
       apply Submodule.mul_induction_on hb
       · intro m hm n hn
@@ -1292,7 +1292,7 @@ theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     obtain ⟨y', hy'⟩ := hJ y mem_J
     use aI * y'
     constructor
-    · apply (nonZeroDivisors R₁).mul_mem haI (mem_non_zero_divisors_iff_ne_zero.mpr _)
+    · apply (nonZeroDivisors R₁).hMul_mem haI (mem_non_zero_divisors_iff_ne_zero.mpr _)
       intro y'_eq_zero
       have : algebraMap R₁ K aJ * y = 0 := by
         rw [← Algebra.smul_def, ← hy', y'_eq_zero, RingHom.map_zero]

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

@@ -1697,7 +1697,7 @@ theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocali
   · rw [mem_canonical_equiv_apply]
     obtain ⟨z, rfl⟩ := (mem_span_singleton _).mp h
     use z • x
-    use (mem_span_singleton _).mpr ⟨z, rfl⟩
+    use(mem_span_singleton _).mpr ⟨z, rfl⟩
     simp [IsLocalization.map_smul]
 #align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingleton
 -/
@@ -1818,7 +1818,7 @@ instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Alg
     [IsFractionRing R K] (I : FractionalIdeal R⁰ K) : (I : Submodule R K).IsPrincipal :=
   by
   obtain ⟨a, aI, -, ha⟩ := exists_eq_span_singleton_mul I
-  use (algebraMap R K a)⁻¹ * algebraMap R K (generator aI)
+  use(algebraMap R K a)⁻¹ * algebraMap R K (generator aI)
   suffices I = span_singleton R⁰ ((algebraMap R K a)⁻¹ * algebraMap R K (generator aI)) by
     rw [span_singleton] at this ; exact congr_arg Subtype.val this
   conv_lhs => rw [ha, ← span_singleton_generator aI]

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Filippo A. E. Nuccio
-
-! This file was ported from Lean 3 source module ring_theory.fractional_ideal
-! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Finprod
 import Mathbin.RingTheory.IntegralClosure
@@ -16,6 +11,8 @@ import Mathbin.RingTheory.Noetherian
 import Mathbin.RingTheory.PrincipalIdealDomain
 import Mathbin.Tactic.FieldSimp
 
+#align_import ring_theory.fractional_ideal from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
+
 /-!
 # Fractional ideals
 
@@ -1175,7 +1172,7 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 #print FractionalIdeal.exists_ne_zero_mem_isInteger /-
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :

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

@@ -132,9 +132,11 @@ not to be confused with `is_localization.coe_submodule : ideal R → submodule R
 instance : Coe (FractionalIdeal S P) (Submodule R P) :=
   ⟨fun I => I.val⟩
 
+#print FractionalIdeal.isFractional /-
 protected theorem isFractional (I : FractionalIdeal S P) : IsFractional S (I : Submodule R P) :=
   I.Prop
 #align fractional_ideal.is_fractional FractionalIdeal.isFractional
+-/
 
 section SetLike
 
@@ -143,15 +145,19 @@ instance : SetLike (FractionalIdeal S P) P
   coe I := ↑(I : Submodule R P)
   coe_injective' := SetLike.coe_injective.comp Subtype.coe_injective
 
+#print FractionalIdeal.mem_coe /-
 @[simp]
 theorem mem_coe {I : FractionalIdeal S P} {x : P} : x ∈ (I : Submodule R P) ↔ x ∈ I :=
   Iff.rfl
 #align fractional_ideal.mem_coe FractionalIdeal.mem_coe
+-/
 
+#print FractionalIdeal.ext /-
 @[ext]
 theorem ext {I J : FractionalIdeal S P} : (∀ x, x ∈ I ↔ x ∈ J) → I = J :=
   SetLike.ext
 #align fractional_ideal.ext FractionalIdeal.ext
+-/
 
 #print FractionalIdeal.copy /-
 /-- Copy of a `fractional_ideal` with a new underlying set equal to the old one.
@@ -161,27 +167,35 @@ protected def copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : Fract
 #align fractional_ideal.copy FractionalIdeal.copy
 -/
 
+#print FractionalIdeal.coe_copy /-
 @[simp]
 theorem coe_copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : ↑(p.copy s hs) = s :=
   rfl
 #align fractional_ideal.coe_copy FractionalIdeal.coe_copy
+-/
 
+#print FractionalIdeal.coe_eq /-
 theorem coe_eq (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : p.copy s hs = p :=
   SetLike.coe_injective hs
 #align fractional_ideal.coe_eq FractionalIdeal.coe_eq
+-/
 
 end SetLike
 
+#print FractionalIdeal.val_eq_coe /-
 @[simp]
 theorem val_eq_coe (I : FractionalIdeal S P) : I.val = I :=
   rfl
 #align fractional_ideal.val_eq_coe FractionalIdeal.val_eq_coe
+-/
 
+#print FractionalIdeal.coe_mk /-
 @[simp, norm_cast]
 theorem coe_mk (I : Submodule R P) (hI : IsFractional S I) :
     (Subtype.mk I hI : Submodule R P) = I :=
   rfl
 #align fractional_ideal.coe_mk FractionalIdeal.coe_mk
+-/
 
 /-! Transfer instances from `submodule R P` to `fractional_ideal S P`. -/
 
@@ -198,10 +212,13 @@ theorem coeToSubmodule_injective : Function.Injective (coe : FractionalIdeal S P
 #align fractional_ideal.coe_to_submodule_injective FractionalIdeal.coeToSubmodule_injective
 -/
 
+#print FractionalIdeal.coeToSubmodule_inj /-
 theorem coeToSubmodule_inj {I J : FractionalIdeal S P} : (I : Submodule R P) = J ↔ I = J :=
   coeToSubmodule_injective.eq_iff
 #align fractional_ideal.coe_to_submodule_inj FractionalIdeal.coeToSubmodule_inj
+-/
 
+#print FractionalIdeal.isFractional_of_le_one /-
 theorem isFractional_of_le_one (I : Submodule R P) (h : I ≤ 1) : IsFractional S I :=
   by
   use 1, S.one_mem
@@ -210,7 +227,9 @@ theorem isFractional_of_le_one (I : Submodule R P) (h : I ≤ 1) : IsFractional
   obtain ⟨b', b'_mem, rfl⟩ := h hb
   exact Set.mem_range_self b'
 #align fractional_ideal.is_fractional_of_le_one FractionalIdeal.isFractional_of_le_one
+-/
 
+#print FractionalIdeal.isFractional_of_le /-
 theorem isFractional_of_le {I : Submodule R P} {J : FractionalIdeal S P} (hIJ : I ≤ J) :
     IsFractional S I := by
   obtain ⟨a, a_mem, ha⟩ := J.is_fractional
@@ -218,6 +237,7 @@ theorem isFractional_of_le {I : Submodule R P} {J : FractionalIdeal S P} (hIJ :
   intro b b_mem
   exact ha b (hIJ b_mem)
 #align fractional_ideal.is_fractional_of_le FractionalIdeal.isFractional_of_le
+-/
 
 -- Is a `coe_t` rather than `coe` to speed up failing inference, see library note [use has_coe_t]
 /-- Map an ideal `I` to a fractional ideal by forgetting `I` is integral.
@@ -233,39 +253,50 @@ instance : CoeTC (Ideal R) (FractionalIdeal S P) :=
     ⟨coeSubmodule P I,
       isFractional_of_le_one _ <| by simpa using coe_submodule_mono P (le_top : I ≤ ⊤)⟩⟩
 
+#print FractionalIdeal.coe_coeIdeal /-
 @[simp, norm_cast]
 theorem coe_coeIdeal (I : Ideal R) :
     ((I : FractionalIdeal S P) : Submodule R P) = coeSubmodule P I :=
   rfl
 #align fractional_ideal.coe_coe_ideal FractionalIdeal.coe_coeIdeal
+-/
 
 variable (S)
 
+#print FractionalIdeal.mem_coeIdeal /-
 @[simp]
 theorem mem_coeIdeal {x : P} {I : Ideal R} :
     x ∈ (I : FractionalIdeal S P) ↔ ∃ x', x' ∈ I ∧ algebraMap R P x' = x :=
   mem_coeSubmodule _ _
 #align fractional_ideal.mem_coe_ideal FractionalIdeal.mem_coeIdeal
+-/
 
+#print FractionalIdeal.mem_coeIdeal_of_mem /-
 theorem mem_coeIdeal_of_mem {x : R} {I : Ideal R} (hx : x ∈ I) :
     algebraMap R P x ∈ (I : FractionalIdeal S P) :=
   (mem_coeIdeal S).mpr ⟨x, hx, rfl⟩
 #align fractional_ideal.mem_coe_ideal_of_mem FractionalIdeal.mem_coeIdeal_of_mem
+-/
 
+#print FractionalIdeal.coeIdeal_le_coeIdeal' /-
 theorem coeIdeal_le_coeIdeal' [IsLocalization S P] (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
     (I : FractionalIdeal S P) ≤ J ↔ I ≤ J :=
   coeSubmodule_le_coeSubmodule h
 #align fractional_ideal.coe_ideal_le_coe_ideal' FractionalIdeal.coeIdeal_le_coeIdeal'
+-/
 
+#print FractionalIdeal.coeIdeal_le_coeIdeal /-
 @[simp]
 theorem coeIdeal_le_coeIdeal (K : Type _) [CommRing K] [Algebra R K] [IsFractionRing R K]
     {I J : Ideal R} : (I : FractionalIdeal R⁰ K) ≤ J ↔ I ≤ J :=
   IsFractionRing.coeSubmodule_le_coeSubmodule
 #align fractional_ideal.coe_ideal_le_coe_ideal FractionalIdeal.coeIdeal_le_coeIdeal
+-/
 
 instance : Zero (FractionalIdeal S P) :=
   ⟨(0 : Ideal R)⟩
 
+#print FractionalIdeal.mem_zero_iff /-
 @[simp]
 theorem mem_zero_iff {x : P} : x ∈ (0 : FractionalIdeal S P) ↔ x = 0 :=
   ⟨fun ⟨x', x'_mem_zero, x'_eq_x⟩ =>
@@ -273,61 +304,76 @@ theorem mem_zero_iff {x : P} : x ∈ (0 : FractionalIdeal S P) ↔ x = 0 :=
     have x'_eq_zero : x' = 0 := x'_mem_zero
     simp [x'_eq_x.symm, x'_eq_zero], fun hx => ⟨0, rfl, by simp [hx]⟩⟩
 #align fractional_ideal.mem_zero_iff FractionalIdeal.mem_zero_iff
+-/
 
 variable {S}
 
+#print FractionalIdeal.coe_zero /-
 @[simp, norm_cast]
 theorem coe_zero : ↑(0 : FractionalIdeal S P) = (⊥ : Submodule R P) :=
   Submodule.ext fun _ => mem_zero_iff S
 #align fractional_ideal.coe_zero FractionalIdeal.coe_zero
+-/
 
+#print FractionalIdeal.coeIdeal_bot /-
 @[simp, norm_cast]
 theorem coeIdeal_bot : ((⊥ : Ideal R) : FractionalIdeal S P) = 0 :=
   rfl
 #align fractional_ideal.coe_ideal_bot FractionalIdeal.coeIdeal_bot
+-/
 
 variable (P)
 
-include loc
-
+#print FractionalIdeal.exists_mem_algebraMap_eq /-
 @[simp]
 theorem exists_mem_algebraMap_eq {x : R} {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (∃ x', x' ∈ I ∧ algebraMap R P x' = algebraMap R P x) ↔ x ∈ I :=
   ⟨fun ⟨x', hx', Eq⟩ => IsLocalization.injective _ h Eq ▸ hx', fun h => ⟨x, h, rfl⟩⟩
 #align fractional_ideal.exists_mem_to_map_eq FractionalIdeal.exists_mem_algebraMap_eq
+-/
 
 variable {P}
 
+#print FractionalIdeal.coeIdeal_injective' /-
 theorem coeIdeal_injective' (h : S ≤ nonZeroDivisors R) :
     Function.Injective (coe : Ideal R → FractionalIdeal S P) := fun _ _ h' =>
   ((coeIdeal_le_coeIdeal' S h).mp h'.le).antisymm ((coeIdeal_le_coeIdeal' S h).mp h'.ge)
 #align fractional_ideal.coe_ideal_injective' FractionalIdeal.coeIdeal_injective'
+-/
 
+#print FractionalIdeal.coeIdeal_inj' /-
 theorem coeIdeal_inj' (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
     (I : FractionalIdeal S P) = J ↔ I = J :=
   (coeIdeal_injective' h).eq_iff
 #align fractional_ideal.coe_ideal_inj' FractionalIdeal.coeIdeal_inj'
+-/
 
+#print FractionalIdeal.coeIdeal_eq_zero' /-
 @[simp]
 theorem coeIdeal_eq_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (I : FractionalIdeal S P) = 0 ↔ I = (⊥ : Ideal R) :=
   coeIdeal_inj' h
 #align fractional_ideal.coe_ideal_eq_zero' FractionalIdeal.coeIdeal_eq_zero'
+-/
 
+#print FractionalIdeal.coeIdeal_ne_zero' /-
 theorem coeIdeal_ne_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (I : FractionalIdeal S P) ≠ 0 ↔ I ≠ (⊥ : Ideal R) :=
   not_iff_not.mpr <| coeIdeal_eq_zero' h
 #align fractional_ideal.coe_ideal_ne_zero' FractionalIdeal.coeIdeal_ne_zero'
+-/
 
-omit loc
-
+#print FractionalIdeal.coeToSubmodule_eq_bot /-
 theorem coeToSubmodule_eq_bot {I : FractionalIdeal S P} : (I : Submodule R P) = ⊥ ↔ I = 0 :=
   ⟨fun h => coeToSubmodule_injective (by simp [h]), fun h => by simp [h]⟩
 #align fractional_ideal.coe_to_submodule_eq_bot FractionalIdeal.coeToSubmodule_eq_bot
+-/
 
+#print FractionalIdeal.coeToSubmodule_ne_bot /-
 theorem coeToSubmodule_ne_bot {I : FractionalIdeal S P} : ↑I ≠ (⊥ : Submodule R P) ↔ I ≠ 0 :=
   not_iff_not.mpr coeToSubmodule_eq_bot
 #align fractional_ideal.coe_to_submodule_ne_bot FractionalIdeal.coeToSubmodule_ne_bot
+-/
 
 instance : Inhabited (FractionalIdeal S P) :=
   ⟨0⟩
@@ -337,25 +383,34 @@ instance : One (FractionalIdeal S P) :=
 
 variable (S)
 
+#print FractionalIdeal.coeIdeal_top /-
 @[simp, norm_cast]
 theorem coeIdeal_top : ((⊤ : Ideal R) : FractionalIdeal S P) = 1 :=
   rfl
 #align fractional_ideal.coe_ideal_top FractionalIdeal.coeIdeal_top
+-/
 
+#print FractionalIdeal.mem_one_iff /-
 theorem mem_one_iff {x : P} : x ∈ (1 : FractionalIdeal S P) ↔ ∃ x' : R, algebraMap R P x' = x :=
   Iff.intro (fun ⟨x', _, h⟩ => ⟨x', h⟩) fun ⟨x', h⟩ => ⟨x', ⟨⟩, h⟩
 #align fractional_ideal.mem_one_iff FractionalIdeal.mem_one_iff
+-/
 
+#print FractionalIdeal.coe_mem_one /-
 theorem coe_mem_one (x : R) : algebraMap R P x ∈ (1 : FractionalIdeal S P) :=
   (mem_one_iff S).mpr ⟨x, rfl⟩
 #align fractional_ideal.coe_mem_one FractionalIdeal.coe_mem_one
+-/
 
+#print FractionalIdeal.one_mem_one /-
 theorem one_mem_one : (1 : P) ∈ (1 : FractionalIdeal S P) :=
   (mem_one_iff S).mpr ⟨1, RingHom.map_one _⟩
 #align fractional_ideal.one_mem_one FractionalIdeal.one_mem_one
+-/
 
 variable {S}
 
+#print FractionalIdeal.coe_one_eq_coeSubmodule_top /-
 /-- `(1 : fractional_ideal S P)` is defined as the R-submodule `f(R) ≤ P`.
 
 However, this is not definitionally equal to `1 : submodule R P`,
@@ -363,11 +418,14 @@ which is proved in the actual `simp` lemma `coe_one`. -/
 theorem coe_one_eq_coeSubmodule_top : ↑(1 : FractionalIdeal S P) = coeSubmodule P (⊤ : Ideal R) :=
   rfl
 #align fractional_ideal.coe_one_eq_coe_submodule_top FractionalIdeal.coe_one_eq_coeSubmodule_top
+-/
 
+#print FractionalIdeal.coe_one /-
 @[simp, norm_cast]
 theorem coe_one : (↑(1 : FractionalIdeal S P) : Submodule R P) = 1 := by
   rw [coe_one_eq_coe_submodule_top, coe_submodule_top]
 #align fractional_ideal.coe_one FractionalIdeal.coe_one
+-/
 
 section Lattice
 
@@ -379,40 +437,53 @@ and ports the lattice structure on submodules to fractional ideals.
 -/
 
 
+#print FractionalIdeal.coe_le_coe /-
 @[simp]
 theorem coe_le_coe {I J : FractionalIdeal S P} :
     (I : Submodule R P) ≤ (J : Submodule R P) ↔ I ≤ J :=
   Iff.rfl
 #align fractional_ideal.coe_le_coe FractionalIdeal.coe_le_coe
+-/
 
+#print FractionalIdeal.zero_le /-
 theorem zero_le (I : FractionalIdeal S P) : 0 ≤ I :=
   by
   intro x hx
   convert Submodule.zero_mem _
   simpa using hx
 #align fractional_ideal.zero_le FractionalIdeal.zero_le
+-/
 
+#print FractionalIdeal.orderBot /-
 instance orderBot : OrderBot (FractionalIdeal S P)
     where
   bot := 0
   bot_le := zero_le
 #align fractional_ideal.order_bot FractionalIdeal.orderBot
+-/
 
+#print FractionalIdeal.bot_eq_zero /-
 @[simp]
 theorem bot_eq_zero : (⊥ : FractionalIdeal S P) = 0 :=
   rfl
 #align fractional_ideal.bot_eq_zero FractionalIdeal.bot_eq_zero
+-/
 
+#print FractionalIdeal.le_zero_iff /-
 @[simp]
 theorem le_zero_iff {I : FractionalIdeal S P} : I ≤ 0 ↔ I = 0 :=
   le_bot_iff
 #align fractional_ideal.le_zero_iff FractionalIdeal.le_zero_iff
+-/
 
+#print FractionalIdeal.eq_zero_iff /-
 theorem eq_zero_iff {I : FractionalIdeal S P} : I = 0 ↔ ∀ x ∈ I, x = (0 : P) :=
   ⟨fun h x hx => by simpa [h, mem_zero_iff] using hx, fun h =>
     le_bot_iff.mp fun x hx => (mem_zero_iff S).mpr (h x hx)⟩
 #align fractional_ideal.eq_zero_iff FractionalIdeal.eq_zero_iff
+-/
 
+#print IsFractional.sup /-
 theorem IsFractional.sup {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I ⊔ J)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
@@ -426,29 +497,36 @@ theorem IsFractional.sup {I J : Submodule R P} :
       · rw [mul_smul]
         exact is_integer_smul (hJ bJ hbJ)⟩
 #align is_fractional.sup IsFractional.sup
+-/
 
+#print IsFractional.inf_right /-
 theorem IsFractional.inf_right {I : Submodule R P} : IsFractional S I → ∀ J, IsFractional S (I ⊓ J)
   | ⟨aI, haI, hI⟩, J =>
     ⟨aI, haI, fun b hb => by
       rcases mem_inf.mp hb with ⟨hbI, hbJ⟩
       exact hI b hbI⟩
 #align is_fractional.inf_right IsFractional.inf_right
+-/
 
 instance : Inf (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊓ J, I.IsFractional.inf_right J⟩⟩
 
+#print FractionalIdeal.coe_inf /-
 @[simp, norm_cast]
 theorem coe_inf (I J : FractionalIdeal S P) : ↑(I ⊓ J) = (I ⊓ J : Submodule R P) :=
   rfl
 #align fractional_ideal.coe_inf FractionalIdeal.coe_inf
+-/
 
 instance : Sup (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊔ J, I.IsFractional.sup J.IsFractional⟩⟩
 
+#print FractionalIdeal.coe_sup /-
 @[norm_cast]
 theorem coe_sup (I J : FractionalIdeal S P) : ↑(I ⊔ J) = (I ⊔ J : Submodule R P) :=
   rfl
 #align fractional_ideal.coe_sup FractionalIdeal.coe_sup
+-/
 
 #print FractionalIdeal.lattice /-
 instance lattice : Lattice (FractionalIdeal S P) :=
@@ -466,21 +544,28 @@ section Semiring
 instance : Add (FractionalIdeal S P) :=
   ⟨(· ⊔ ·)⟩
 
+#print FractionalIdeal.sup_eq_add /-
 @[simp]
 theorem sup_eq_add (I J : FractionalIdeal S P) : I ⊔ J = I + J :=
   rfl
 #align fractional_ideal.sup_eq_add FractionalIdeal.sup_eq_add
+-/
 
+#print FractionalIdeal.coe_add /-
 @[simp, norm_cast]
 theorem coe_add (I J : FractionalIdeal S P) : (↑(I + J) : Submodule R P) = I + J :=
   rfl
 #align fractional_ideal.coe_add FractionalIdeal.coe_add
+-/
 
+#print FractionalIdeal.coeIdeal_sup /-
 @[simp, norm_cast]
 theorem coeIdeal_sup (I J : Ideal R) : ↑(I ⊔ J) = (I + J : FractionalIdeal S P) :=
   coeToSubmodule_injective <| coeSubmodule_sup _ _ _
 #align fractional_ideal.coe_ideal_sup FractionalIdeal.coeIdeal_sup
+-/
 
+#print IsFractional.nsmul /-
 theorem IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
   | 0, _ => by
@@ -491,14 +576,18 @@ theorem IsFractional.nsmul {I : Submodule R P} :
     rw [succ_nsmul]
     exact h.sup (_root_.is_fractional.nsmul n h)
 #align is_fractional.nsmul IsFractional.nsmul
+-/
 
 instance : SMul ℕ (FractionalIdeal S P) where smul n I := ⟨n • I, I.IsFractional.nsmul n⟩
 
+#print FractionalIdeal.coe_nsmul /-
 @[norm_cast]
 theorem coe_nsmul (n : ℕ) (I : FractionalIdeal S P) : (↑(n • I) : Submodule R P) = n • I :=
   rfl
 #align fractional_ideal.coe_nsmul FractionalIdeal.coe_nsmul
+-/
 
+#print IsFractional.mul /-
 theorem IsFractional.mul {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I * J : Submodule R P)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
@@ -514,12 +603,15 @@ theorem IsFractional.mul {I J : Submodule R P} :
         rw [smul_add]
         apply is_integer_add hx hy⟩
 #align is_fractional.mul IsFractional.mul
+-/
 
+#print IsFractional.pow /-
 theorem IsFractional.pow {I : Submodule R P} (h : IsFractional S I) :
     ∀ n : ℕ, IsFractional S (I ^ n : Submodule R P)
   | 0 => isFractional_of_le_one _ (pow_zero _).le
   | n + 1 => (pow_succ I n).symm ▸ h.mul (_root_.is_fractional.pow n)
 #align is_fractional.pow IsFractional.pow
+-/
 
 #print FractionalIdeal.mul /-
 /-- `fractional_ideal.mul` is the product of two fractional ideals,
@@ -539,57 +631,76 @@ irreducible_def mul (I J : FractionalIdeal S P) : FractionalIdeal S P :=
 instance : Mul (FractionalIdeal S P) :=
   ⟨fun I J => mul I J⟩
 
+#print FractionalIdeal.mul_eq_mul /-
 @[simp]
 theorem mul_eq_mul (I J : FractionalIdeal S P) : mul I J = I * J :=
   rfl
 #align fractional_ideal.mul_eq_mul FractionalIdeal.mul_eq_mul
+-/
 
+#print FractionalIdeal.mul_def /-
 theorem mul_def (I J : FractionalIdeal S P) : I * J = ⟨I * J, I.IsFractional.mul J.IsFractional⟩ :=
   by simp only [← mul_eq_mul, mul]
 #align fractional_ideal.mul_def FractionalIdeal.mul_def
+-/
 
+#print FractionalIdeal.coe_mul /-
 @[simp, norm_cast]
 theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I * J := by
   simp only [mul_def]; rfl
 #align fractional_ideal.coe_mul FractionalIdeal.coe_mul
+-/
 
+#print FractionalIdeal.coeIdeal_mul /-
 @[simp, norm_cast]
 theorem coeIdeal_mul (I J : Ideal R) : (↑(I * J) : FractionalIdeal S P) = I * J :=
   by
   simp only [mul_def]
   exact coe_to_submodule_injective (coe_submodule_mul _ _ _)
 #align fractional_ideal.coe_ideal_mul FractionalIdeal.coeIdeal_mul
+-/
 
+#print FractionalIdeal.mul_left_mono /-
 theorem mul_left_mono (I : FractionalIdeal S P) : Monotone ((· * ·) I) :=
   by
   intro J J' h
   simp only [mul_def]
   exact mul_le.mpr fun x hx y hy => mul_mem_mul hx (h hy)
 #align fractional_ideal.mul_left_mono FractionalIdeal.mul_left_mono
+-/
 
+#print FractionalIdeal.mul_right_mono /-
 theorem mul_right_mono (I : FractionalIdeal S P) : Monotone fun J => J * I :=
   by
   intro J J' h
   simp only [mul_def]
   exact mul_le.mpr fun x hx y hy => mul_mem_mul (h hx) hy
 #align fractional_ideal.mul_right_mono FractionalIdeal.mul_right_mono
+-/
 
+#print FractionalIdeal.mul_mem_mul /-
 theorem mul_mem_mul {I J : FractionalIdeal S P} {i j : P} (hi : i ∈ I) (hj : j ∈ J) :
     i * j ∈ I * J := by simp only [mul_def]; exact Submodule.mul_mem_mul hi hj
 #align fractional_ideal.mul_mem_mul FractionalIdeal.mul_mem_mul
+-/
 
+#print FractionalIdeal.mul_le /-
 theorem mul_le {I J K : FractionalIdeal S P} : I * J ≤ K ↔ ∀ i ∈ I, ∀ j ∈ J, i * j ∈ K := by
   simp only [mul_def]; exact Submodule.mul_le
 #align fractional_ideal.mul_le FractionalIdeal.mul_le
+-/
 
 instance : Pow (FractionalIdeal S P) ℕ :=
   ⟨fun I n => ⟨I ^ n, I.IsFractional.pow n⟩⟩
 
+#print FractionalIdeal.coe_pow /-
 @[simp, norm_cast]
 theorem coe_pow (I : FractionalIdeal S P) (n : ℕ) : ↑(I ^ n) = (I ^ n : Submodule R P) :=
   rfl
 #align fractional_ideal.coe_pow FractionalIdeal.coe_pow
+-/
 
+#print FractionalIdeal.mul_induction_on /-
 @[elab_as_elim]
 protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop} {r : P}
     (hr : r ∈ I * J) (hm : ∀ i ∈ I, ∀ j ∈ J, C (i * j)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
@@ -597,13 +708,16 @@ protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop}
   simp only [mul_def] at hr 
   exact Submodule.mul_induction_on hr hm ha
 #align fractional_ideal.mul_induction_on FractionalIdeal.mul_induction_on
+-/
 
 instance : NatCast (FractionalIdeal S P) :=
   ⟨Nat.unaryCast⟩
 
+#print FractionalIdeal.coe_nat_cast /-
 theorem coe_nat_cast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
   show ↑n.unaryCast = ↑n by induction n <;> simp [*, Nat.unaryCast]
 #align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_cast
+-/
 
 instance : CommSemiring (FractionalIdeal S P) :=
   Function.Injective.commSemiring coe Subtype.coe_injective coe_zero coe_one coe_add coe_mul
@@ -623,33 +737,44 @@ variable {S P}
 
 section Order
 
+#print FractionalIdeal.add_le_add_left /-
 theorem add_le_add_left {I J : FractionalIdeal S P} (hIJ : I ≤ J) (J' : FractionalIdeal S P) :
     J' + I ≤ J' + J :=
   sup_le_sup_left hIJ J'
 #align fractional_ideal.add_le_add_left FractionalIdeal.add_le_add_left
+-/
 
+#print FractionalIdeal.mul_le_mul_left /-
 theorem mul_le_mul_left {I J : FractionalIdeal S P} (hIJ : I ≤ J) (J' : FractionalIdeal S P) :
     J' * I ≤ J' * J :=
   mul_le.mpr fun k hk j hj => mul_mem_mul hk (hIJ hj)
 #align fractional_ideal.mul_le_mul_left FractionalIdeal.mul_le_mul_left
+-/
 
+#print FractionalIdeal.le_self_mul_self /-
 theorem le_self_mul_self {I : FractionalIdeal S P} (hI : 1 ≤ I) : I ≤ I * I :=
   by
   convert mul_left_mono I hI
   exact (mul_one I).symm
 #align fractional_ideal.le_self_mul_self FractionalIdeal.le_self_mul_self
+-/
 
+#print FractionalIdeal.mul_self_le_self /-
 theorem mul_self_le_self {I : FractionalIdeal S P} (hI : I ≤ 1) : I * I ≤ I :=
   by
   convert mul_left_mono I hI
   exact (mul_one I).symm
 #align fractional_ideal.mul_self_le_self FractionalIdeal.mul_self_le_self
+-/
 
+#print FractionalIdeal.coeIdeal_le_one /-
 theorem coeIdeal_le_one {I : Ideal R} : (I : FractionalIdeal S P) ≤ 1 := fun x hx =>
   let ⟨y, _, hy⟩ := (mem_coeIdeal S).mp hx
   (mem_one_iff S).mpr ⟨y, hy⟩
 #align fractional_ideal.coe_ideal_le_one FractionalIdeal.coeIdeal_le_one
+-/
 
+#print FractionalIdeal.le_one_iff_exists_coeIdeal /-
 theorem le_one_iff_exists_coeIdeal {J : FractionalIdeal S P} :
     J ≤ (1 : FractionalIdeal S P) ↔ ∃ I : Ideal R, ↑I = J :=
   by
@@ -676,11 +801,14 @@ theorem le_one_iff_exists_coeIdeal {J : FractionalIdeal S P} :
     rw [← hI]
     apply coe_ideal_le_one
 #align fractional_ideal.le_one_iff_exists_coe_ideal FractionalIdeal.le_one_iff_exists_coeIdeal
+-/
 
+#print FractionalIdeal.one_le /-
 @[simp]
 theorem one_le {I : FractionalIdeal S P} : 1 ≤ I ↔ (1 : P) ∈ I := by
   rw [← coe_le_coe, coe_one, Submodule.one_le, mem_coe]
 #align fractional_ideal.one_le FractionalIdeal.one_le
+-/
 
 variable (S P)
 
@@ -697,17 +825,21 @@ def coeIdealHom : Ideal R →+* FractionalIdeal S P
 #align fractional_ideal.coe_ideal_hom FractionalIdeal.coeIdealHom
 -/
 
+#print FractionalIdeal.coeIdeal_pow /-
 theorem coeIdeal_pow (I : Ideal R) (n : ℕ) : (↑(I ^ n) : FractionalIdeal S P) = I ^ n :=
   (coeIdealHom S P).map_pow _ n
 #align fractional_ideal.coe_ideal_pow FractionalIdeal.coeIdeal_pow
+-/
 
 open scoped BigOperators
 
+#print FractionalIdeal.coeIdeal_finprod /-
 theorem coeIdeal_finprod [IsLocalization S P] {α : Sort _} {f : α → Ideal R}
     (hS : S ≤ nonZeroDivisors R) :
     ((∏ᶠ a : α, f a : Ideal R) : FractionalIdeal S P) = ∏ᶠ a : α, (f a : FractionalIdeal S P) :=
   MonoidHom.map_finprod_of_injective (coeIdealHom S P).toMonoidHom (coeIdeal_injective' hS) f
 #align fractional_ideal.coe_ideal_finprod FractionalIdeal.coeIdeal_finprod
+-/
 
 end Order
 
@@ -715,6 +847,7 @@ variable {P' : Type _} [CommRing P'] [Algebra R P'] [loc' : IsLocalization S P']
 
 variable {P'' : Type _} [CommRing P''] [Algebra R P''] [loc'' : IsLocalization S P'']
 
+#print IsFractional.map /-
 theorem IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
     IsFractional S I → IsFractional S (Submodule.map g.toLinearMap I)
   | ⟨a, a_nonzero, hI⟩ =>
@@ -725,6 +858,7 @@ theorem IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
       use x
       erw [← g.commutes, hx, g.map_smul, hb']⟩
 #align is_fractional.map IsFractional.map
+-/
 
 #print FractionalIdeal.map /-
 /-- `I.map g` is the pushforward of the fractional ideal `I` along the algebra morphism `g` -/
@@ -733,17 +867,21 @@ def map (g : P →ₐ[R] P') : FractionalIdeal S P → FractionalIdeal S P' := f
 #align fractional_ideal.map FractionalIdeal.map
 -/
 
+#print FractionalIdeal.coe_map /-
 @[simp, norm_cast]
 theorem coe_map (g : P →ₐ[R] P') (I : FractionalIdeal S P) :
     ↑(map g I) = Submodule.map g.toLinearMap I :=
   rfl
 #align fractional_ideal.coe_map FractionalIdeal.coe_map
+-/
 
+#print FractionalIdeal.mem_map /-
 @[simp]
 theorem mem_map {I : FractionalIdeal S P} {g : P →ₐ[R] P'} {y : P'} :
     y ∈ I.map g ↔ ∃ x, x ∈ I ∧ g x = y :=
   Submodule.mem_map
 #align fractional_ideal.mem_map FractionalIdeal.mem_map
+-/
 
 variable (I J : FractionalIdeal S P) (g : P →ₐ[R] P')
 
@@ -754,11 +892,14 @@ theorem map_id : I.map (AlgHom.id _ _) = I :=
 #align fractional_ideal.map_id FractionalIdeal.map_id
 -/
 
+#print FractionalIdeal.map_comp /-
 @[simp]
 theorem map_comp (g' : P' →ₐ[R] P'') : I.map (g'.comp g) = (I.map g).map g' :=
   coeToSubmodule_injective (Submodule.map_comp g.toLinearMap g'.toLinearMap I)
 #align fractional_ideal.map_comp FractionalIdeal.map_comp
+-/
 
+#print FractionalIdeal.map_coeIdeal /-
 @[simp, norm_cast]
 theorem map_coeIdeal (I : Ideal R) : (I : FractionalIdeal S P).map g = I :=
   by
@@ -770,50 +911,68 @@ theorem map_coeIdeal (I : Ideal R) : (I : FractionalIdeal S P).map g = I :=
   · rintro ⟨y, hy, rfl⟩
     exact ⟨_, ⟨y, hy, rfl⟩, g.commutes y⟩
 #align fractional_ideal.map_coe_ideal FractionalIdeal.map_coeIdeal
+-/
 
+#print FractionalIdeal.map_one /-
 @[simp]
 theorem map_one : (1 : FractionalIdeal S P).map g = 1 :=
   map_coeIdeal g ⊤
 #align fractional_ideal.map_one FractionalIdeal.map_one
+-/
 
+#print FractionalIdeal.map_zero /-
 @[simp]
 theorem map_zero : (0 : FractionalIdeal S P).map g = 0 :=
   map_coeIdeal g 0
 #align fractional_ideal.map_zero FractionalIdeal.map_zero
+-/
 
+#print FractionalIdeal.map_add /-
 @[simp]
 theorem map_add : (I + J).map g = I.map g + J.map g :=
   coeToSubmodule_injective (Submodule.map_sup _ _ _)
 #align fractional_ideal.map_add FractionalIdeal.map_add
+-/
 
+#print FractionalIdeal.map_mul /-
 @[simp]
 theorem map_mul : (I * J).map g = I.map g * J.map g :=
   by
   simp only [mul_def]
   exact coe_to_submodule_injective (Submodule.map_mul _ _ _)
 #align fractional_ideal.map_mul FractionalIdeal.map_mul
+-/
 
+#print FractionalIdeal.map_map_symm /-
 @[simp]
 theorem map_map_symm (g : P ≃ₐ[R] P') : (I.map (g : P →ₐ[R] P')).map (g.symm : P' →ₐ[R] P) = I := by
   rw [← map_comp, g.symm_comp, map_id]
 #align fractional_ideal.map_map_symm FractionalIdeal.map_map_symm
+-/
 
+#print FractionalIdeal.map_symm_map /-
 @[simp]
 theorem map_symm_map (I : FractionalIdeal S P') (g : P ≃ₐ[R] P') :
     (I.map (g.symm : P' →ₐ[R] P)).map (g : P →ₐ[R] P') = I := by
   rw [← map_comp, g.comp_symm, map_id]
 #align fractional_ideal.map_symm_map FractionalIdeal.map_symm_map
+-/
 
+#print FractionalIdeal.map_mem_map /-
 theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I : FractionalIdeal S P} :
     f x ∈ map f I ↔ x ∈ I :=
   mem_map.trans ⟨fun ⟨x', hx', x'_eq⟩ => h x'_eq ▸ hx', fun h => ⟨x, h, rfl⟩⟩
 #align fractional_ideal.map_mem_map FractionalIdeal.map_mem_map
+-/
 
+#print FractionalIdeal.map_injective /-
 theorem map_injective (f : P →ₐ[R] P') (h : Function.Injective f) :
     Function.Injective (map f : FractionalIdeal S P → FractionalIdeal S P') := fun I J hIJ =>
   ext fun x => (map_mem_map h).symm.trans (hIJ.symm ▸ map_mem_map h)
 #align fractional_ideal.map_injective FractionalIdeal.map_injective
+-/
 
+#print FractionalIdeal.mapEquiv /-
 /-- If `g` is an equivalence, `map g` is an isomorphism -/
 def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S P'
     where
@@ -824,29 +983,39 @@ def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S
   left_inv I := by rw [← map_comp, AlgEquiv.symm_comp, map_id]
   right_inv I := by rw [← map_comp, AlgEquiv.comp_symm, map_id]
 #align fractional_ideal.map_equiv FractionalIdeal.mapEquiv
+-/
 
+#print FractionalIdeal.coeFun_mapEquiv /-
 @[simp]
 theorem coeFun_mapEquiv (g : P ≃ₐ[R] P') :
     (mapEquiv g : FractionalIdeal S P → FractionalIdeal S P') = map g :=
   rfl
 #align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coeFun_mapEquiv
+-/
 
+#print FractionalIdeal.mapEquiv_apply /-
 @[simp]
 theorem mapEquiv_apply (g : P ≃ₐ[R] P') (I : FractionalIdeal S P) : mapEquiv g I = map (↑g) I :=
   rfl
 #align fractional_ideal.map_equiv_apply FractionalIdeal.mapEquiv_apply
+-/
 
+#print FractionalIdeal.mapEquiv_symm /-
 @[simp]
 theorem mapEquiv_symm (g : P ≃ₐ[R] P') :
     ((mapEquiv g).symm : FractionalIdeal S P' ≃+* _) = mapEquiv g.symm :=
   rfl
 #align fractional_ideal.map_equiv_symm FractionalIdeal.mapEquiv_symm
+-/
 
+#print FractionalIdeal.mapEquiv_refl /-
 @[simp]
 theorem mapEquiv_refl : mapEquiv AlgEquiv.refl = RingEquiv.refl (FractionalIdeal S P) :=
   RingEquiv.ext fun x => by simp
 #align fractional_ideal.map_equiv_refl FractionalIdeal.mapEquiv_refl
+-/
 
+#print FractionalIdeal.isFractional_span_iff /-
 theorem isFractional_span_iff {s : Set P} :
     IsFractional S (span R s) ↔ ∃ a ∈ S, ∀ b : P, b ∈ s → IsInteger R (a • b) :=
   ⟨fun ⟨a, a_mem, h⟩ => ⟨a, a_mem, fun b hb => h b (subset_span hb)⟩, fun ⟨a, a_mem, h⟩ =>
@@ -855,9 +1024,9 @@ theorem isFractional_span_iff {s : Set P} :
         (fun x y hx hy => by rw [smul_add]; exact is_integer_add hx hy) fun s x hx => by
         rw [smul_comm]; exact is_integer_smul hx⟩⟩
 #align fractional_ideal.is_fractional_span_iff FractionalIdeal.isFractional_span_iff
+-/
 
-include loc
-
+#print FractionalIdeal.isFractional_of_fg /-
 theorem isFractional_of_fg {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
   by
   rcases hI with ⟨I, rfl⟩
@@ -865,20 +1034,23 @@ theorem isFractional_of_fg {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
   rw [is_fractional_span_iff]
   exact ⟨s, hs1, hs⟩
 #align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fg
+-/
 
-omit loc
-
+#print FractionalIdeal.mem_span_mul_finite_of_mem_mul /-
 theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx : x ∈ I * J) :
     ∃ T T' : Finset P, (T : Set P) ⊆ I ∧ (T' : Set P) ⊆ J ∧ x ∈ span R (T * T' : Set P) :=
   Submodule.mem_span_mul_finite_of_mem_mul (by simpa using mem_coe.mpr hx)
 #align fractional_ideal.mem_span_mul_finite_of_mem_mul FractionalIdeal.mem_span_mul_finite_of_mem_mul
+-/
 
 variable (S)
 
+#print FractionalIdeal.coeIdeal_fg /-
 theorem coeIdeal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
     FG ((I : FractionalIdeal S P) : Submodule R P) ↔ I.FG :=
   coeSubmodule_fg _ inj _
 #align fractional_ideal.coe_ideal_fg FractionalIdeal.coeIdeal_fg
+-/
 
 variable {S}
 
@@ -888,19 +1060,22 @@ theorem fg_unit (I : (FractionalIdeal S P)ˣ) : FG (I : Submodule R P) :=
 #align fractional_ideal.fg_unit FractionalIdeal.fg_unit
 -/
 
+#print FractionalIdeal.fg_of_isUnit /-
 theorem fg_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : FG (I : Submodule R P) :=
   fg_unit h.Unit
 #align fractional_ideal.fg_of_is_unit FractionalIdeal.fg_of_isUnit
+-/
 
+#print Ideal.fg_of_isUnit /-
 theorem Ideal.fg_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
     (h : IsUnit (I : FractionalIdeal S P)) : I.FG := by rw [← coe_ideal_fg S inj I];
   exact fg_of_is_unit I h
 #align ideal.fg_of_is_unit Ideal.fg_of_isUnit
+-/
 
 variable (S P P')
 
-include loc loc'
-
+#print FractionalIdeal.canonicalEquiv /-
 /-- `canonical_equiv f f'` is the canonical equivalence between the fractional
 ideals in `P` and in `P'` -/
 noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* FractionalIdeal S P' :=
@@ -910,7 +1085,9 @@ noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* Fractio
         (show S.map _ = S by rw [RingEquiv.toMonoidHom_refl, Submonoid.map_id]) with
       commutes' := fun r => ringEquivOfRingEquiv_eq _ _ }
 #align fractional_ideal.canonical_equiv FractionalIdeal.canonicalEquiv
+-/
 
+#print FractionalIdeal.mem_canonicalEquiv_apply /-
 @[simp]
 theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
     x ∈ canonicalEquiv S P P' I ↔
@@ -922,7 +1099,9 @@ theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
   rw [canonical_equiv, map_equiv_apply, mem_map]
   exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
 #align fractional_ideal.mem_canonical_equiv_apply FractionalIdeal.mem_canonicalEquiv_apply
+-/
 
+#print FractionalIdeal.canonicalEquiv_symm /-
 @[simp]
 theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P' P :=
   RingEquiv.ext fun I =>
@@ -932,11 +1111,15 @@ theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P'
         mem_map]
       exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
 #align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symm
+-/
 
+#print FractionalIdeal.canonicalEquiv_flip /-
 theorem canonicalEquiv_flip (I) : canonicalEquiv S P P' (canonicalEquiv S P' P I) = I := by
   rw [← canonical_equiv_symm, RingEquiv.symm_apply_apply]
 #align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flip
+-/
 
+#print FractionalIdeal.canonicalEquiv_canonicalEquiv /-
 @[simp]
 theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] (I : FractionalIdeal S P) :
@@ -947,20 +1130,24 @@ theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P
     exists_prop, exists_exists_and_eq_and]
   rfl
 #align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquiv
+-/
 
+#print FractionalIdeal.canonicalEquiv_trans_canonicalEquiv /-
 theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] :
     (canonicalEquiv S P P').trans (canonicalEquiv S P' P'') = canonicalEquiv S P P'' :=
   RingEquiv.ext (canonicalEquiv_canonicalEquiv S P P' P'')
 #align fractional_ideal.canonical_equiv_trans_canonical_equiv FractionalIdeal.canonicalEquiv_trans_canonicalEquiv
+-/
 
+#print FractionalIdeal.canonicalEquiv_coeIdeal /-
 @[simp]
 theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I := by ext;
   simp [IsLocalization.map_eq]
 #align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coeIdeal
+-/
 
-omit loc'
-
+#print FractionalIdeal.canonicalEquiv_self /-
 @[simp]
 theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ :=
   by
@@ -968,6 +1155,7 @@ theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ :=
   convert (canonical_equiv S P P).symm_trans_self
   exact (canonical_equiv_symm S P P).symm
 #align fractional_ideal.canonical_equiv_self FractionalIdeal.canonicalEquiv_self
+-/
 
 end Semiring
 
@@ -988,6 +1176,7 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
+#print FractionalIdeal.exists_ne_zero_mem_isInteger /-
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
     ∃ (x : _) (_ : x ≠ (0 : R)), algebraMap R K x ∈ I :=
@@ -1002,7 +1191,9 @@ theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
   · rw [hx]
     exact smul_mem _ _ y_mem
 #align fractional_ideal.exists_ne_zero_mem_is_integer FractionalIdeal.exists_ne_zero_mem_isInteger
+-/
 
+#print FractionalIdeal.map_ne_zero /-
 theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 :=
   by
   obtain ⟨x, x_ne_zero, hx⟩ := exists_ne_zero_mem_is_integer hI
@@ -1010,38 +1201,53 @@ theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 :=
   refine' is_fraction_ring.to_map_eq_zero_iff.mp (eq_zero_iff.mp map_eq_zero _ (mem_map.mpr _))
   exact ⟨algebraMap R K x, hx, h.commutes x⟩
 #align fractional_ideal.map_ne_zero FractionalIdeal.map_ne_zero
+-/
 
+#print FractionalIdeal.map_eq_zero_iff /-
 @[simp]
 theorem map_eq_zero_iff [Nontrivial R] : I.map h = 0 ↔ I = 0 :=
   ⟨imp_of_not_imp_not _ _ (map_ne_zero _), fun hI => hI.symm ▸ map_zero h⟩
 #align fractional_ideal.map_eq_zero_iff FractionalIdeal.map_eq_zero_iff
+-/
 
+#print FractionalIdeal.coeIdeal_injective /-
 theorem coeIdeal_injective : Function.Injective (coe : Ideal R → FractionalIdeal R⁰ K) :=
   coeIdeal_injective' le_rfl
 #align fractional_ideal.coe_ideal_injective FractionalIdeal.coeIdeal_injective
+-/
 
+#print FractionalIdeal.coeIdeal_inj /-
 theorem coeIdeal_inj {I J : Ideal R} :
     (I : FractionalIdeal R⁰ K) = (J : FractionalIdeal R⁰ K) ↔ I = J :=
   coeIdeal_inj' le_rfl
 #align fractional_ideal.coe_ideal_inj FractionalIdeal.coeIdeal_inj
+-/
 
+#print FractionalIdeal.coeIdeal_eq_zero /-
 @[simp]
 theorem coeIdeal_eq_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 0 ↔ I = ⊥ :=
   coeIdeal_eq_zero' le_rfl
 #align fractional_ideal.coe_ideal_eq_zero FractionalIdeal.coeIdeal_eq_zero
+-/
 
+#print FractionalIdeal.coeIdeal_ne_zero /-
 theorem coeIdeal_ne_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 0 ↔ I ≠ ⊥ :=
   coeIdeal_ne_zero' le_rfl
 #align fractional_ideal.coe_ideal_ne_zero FractionalIdeal.coeIdeal_ne_zero
+-/
 
+#print FractionalIdeal.coeIdeal_eq_one /-
 @[simp]
 theorem coeIdeal_eq_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 1 ↔ I = 1 := by
   simpa only [Ideal.one_eq_top] using coe_ideal_inj
 #align fractional_ideal.coe_ideal_eq_one FractionalIdeal.coeIdeal_eq_one
+-/
 
+#print FractionalIdeal.coeIdeal_ne_one /-
 theorem coeIdeal_ne_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 1 ↔ I ≠ 1 :=
   not_iff_not.mpr coeIdeal_eq_one
 #align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coeIdeal_ne_one
+-/
 
 end IsFractionRing
 
@@ -1071,14 +1277,15 @@ instance : Nontrivial (FractionalIdeal R₁⁰ K) :=
         simpa only [h] using coe_mem_one R₁⁰ 1
       one_ne_zero ((mem_zero_iff _).mp this)⟩⟩
 
+#print FractionalIdeal.ne_zero_of_mul_eq_one /-
 theorem ne_zero_of_mul_eq_one (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : I ≠ 0 := fun hI =>
   zero_ne_one' (FractionalIdeal R₁⁰ K) (by convert h; simp [hI])
 #align fractional_ideal.ne_zero_of_mul_eq_one FractionalIdeal.ne_zero_of_mul_eq_one
+-/
 
 variable [IsDomain R₁]
 
-include frac
-
+#print IsFractional.div_of_nonzero /-
 theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     IsFractional R₁⁰ I → IsFractional R₁⁰ J → J ≠ 0 → IsFractional R₁⁰ (I / J)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩, h =>
@@ -1102,39 +1309,51 @@ theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     convert hI _ (hb _ (Submodule.smul_mem _ aJ mem_J)) using 1
     rw [← hy', mul_comm b, ← Algebra.smul_def, mul_smul]
 #align is_fractional.div_of_nonzero IsFractional.div_of_nonzero
+-/
 
+#print FractionalIdeal.fractional_div_of_nonzero /-
 theorem fractional_div_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     IsFractional R₁⁰ (I / J : Submodule R₁ K) :=
   I.IsFractional.div_of_nonzero J.IsFractional fun H =>
     h <| coeToSubmodule_injective <| H.trans coe_zero.symm
 #align fractional_ideal.fractional_div_of_nonzero FractionalIdeal.fractional_div_of_nonzero
+-/
 
 noncomputable instance : Div (FractionalIdeal R₁⁰ K) :=
   ⟨fun I J => if h : J = 0 then 0 else ⟨I / J, fractional_div_of_nonzero h⟩⟩
 
 variable {I J : FractionalIdeal R₁⁰ K} [J ≠ 0]
 
+#print FractionalIdeal.div_zero /-
 @[simp]
 theorem div_zero {I : FractionalIdeal R₁⁰ K} : I / 0 = 0 :=
   dif_pos rfl
 #align fractional_ideal.div_zero FractionalIdeal.div_zero
+-/
 
+#print FractionalIdeal.div_nonzero /-
 theorem div_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     I / J = ⟨I / J, fractional_div_of_nonzero h⟩ :=
   dif_neg h
 #align fractional_ideal.div_nonzero FractionalIdeal.div_nonzero
+-/
 
+#print FractionalIdeal.coe_div /-
 @[simp]
 theorem coe_div {I J : FractionalIdeal R₁⁰ K} (hJ : J ≠ 0) :
     (↑(I / J) : Submodule R₁ K) = ↑I / (↑J : Submodule R₁ K) :=
   congr_arg _ (dif_neg hJ)
 #align fractional_ideal.coe_div FractionalIdeal.coe_div
+-/
 
+#print FractionalIdeal.mem_div_iff_of_nonzero /-
 theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {x} :
     x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I := by rw [div_nonzero h];
   exact Submodule.mem_div_iff_forall_mul_mem
 #align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzero
+-/
 
+#print FractionalIdeal.mul_one_div_le_one /-
 theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :=
   by
   by_cases hI : I = 0
@@ -1143,7 +1362,9 @@ theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :
   · rw [← coe_le_coe, coe_mul, coe_div hI, coe_one]
     apply Submodule.mul_one_div_le_one
 #align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_one
+-/
 
+#print FractionalIdeal.le_self_mul_one_div /-
 theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
     I ≤ I * (1 / I) := by
   by_cases hI_nz : I = 0
@@ -1152,20 +1373,26 @@ theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : Fra
     rw [← coe_le_coe, coe_one] at hI 
     exact Submodule.le_self_mul_one_div hI
 #align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_div
+-/
 
+#print FractionalIdeal.le_div_iff_of_nonzero /-
 theorem le_div_iff_of_nonzero {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ ∀ x ∈ I, ∀ y ∈ J', x * y ∈ J :=
   ⟨fun h x hx => (mem_div_iff_of_nonzero hJ').mp (h hx), fun h x hx =>
     (mem_div_iff_of_nonzero hJ').mpr (h x hx)⟩
 #align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzero
+-/
 
+#print FractionalIdeal.le_div_iff_mul_le /-
 theorem le_div_iff_mul_le {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ I * J' ≤ J := by
   rw [div_nonzero hJ']
   convert Submodule.le_div_iff_mul_le using 1
   rw [← coe_mul, coe_le_coe]
 #align fractional_ideal.le_div_iff_mul_le FractionalIdeal.le_div_iff_mul_le
+-/
 
+#print FractionalIdeal.div_one /-
 @[simp]
 theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I :=
   by
@@ -1179,7 +1406,9 @@ theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I :=
     convert Submodule.smul_mem _ y' h
     exact (Algebra.smul_def _ _).symm
 #align fractional_ideal.div_one FractionalIdeal.div_one
+-/
 
+#print FractionalIdeal.eq_one_div_of_mul_eq_one_right /-
 theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : J = 1 / I :=
   by
   have hI : I ≠ 0 := ne_zero_of_mul_eq_one I J h
@@ -1200,13 +1429,17 @@ theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I
   rw [mul_comm]
   exact mul_mem_mul hx hy
 #align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_right
+-/
 
+#print FractionalIdeal.mul_div_self_cancel_iff /-
 theorem mul_div_self_cancel_iff {I : FractionalIdeal R₁⁰ K} : I * (1 / I) = 1 ↔ ∃ J, I * J = 1 :=
   ⟨fun h => ⟨1 / I, h⟩, fun ⟨J, hJ⟩ => by rwa [← eq_one_div_of_mul_eq_one_right I J hJ]⟩
 #align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iff
+-/
 
 variable {K' : Type _} [Field K'] [Algebra R₁ K'] [IsFractionRing R₁ K']
 
+#print FractionalIdeal.map_div /-
 @[simp]
 theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     (I / J).map (h : K →ₐ[R₁] K') = I.map h / J.map h :=
@@ -1216,11 +1449,14 @@ theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
   · apply coe_to_submodule_injective
     simp [div_nonzero H, div_nonzero (map_ne_zero _ H), Submodule.map_div]
 #align fractional_ideal.map_div FractionalIdeal.map_div
+-/
 
+#print FractionalIdeal.map_one_div /-
 @[simp]
 theorem map_one_div (I : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     (1 / I).map (h : K →ₐ[R₁] K') = 1 / I.map h := by rw [map_div, map_one]
 #align fractional_ideal.map_one_div FractionalIdeal.map_one_div
+-/
 
 end Quotient
 
@@ -1230,6 +1466,7 @@ variable {R₁ K L : Type _} [CommRing R₁] [Field K] [Field L]
 
 variable [Algebra R₁ K] [IsFractionRing R₁ K] [Algebra K L] [IsFractionRing K L]
 
+#print FractionalIdeal.eq_zero_or_one /-
 theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
   by
   rw [or_iff_not_imp_left]
@@ -1246,11 +1483,14 @@ theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
     rw [← div_mul_cancel x y_ne, RingHom.map_mul, ← Algebra.smul_def]
     exact Submodule.smul_mem I _ y_mem
 #align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_one
+-/
 
+#print FractionalIdeal.eq_zero_or_one_of_isField /-
 theorem eq_zero_or_one_of_isField (hF : IsField R₁) (I : FractionalIdeal R₁⁰ K) : I = 0 ∨ I = 1 :=
   letI : Field R₁ := hF.to_field
   eq_zero_or_one I
 #align fractional_ideal.eq_zero_or_one_of_is_field FractionalIdeal.eq_zero_or_one_of_isField
+-/
 
 end Field
 
@@ -1281,25 +1521,29 @@ def spanFinset {ι : Type _} (s : Finset ι) (f : ι → K) : FractionalIdeal R
 
 variable {R₁}
 
+#print FractionalIdeal.spanFinset_eq_zero /-
 @[simp]
 theorem spanFinset_eq_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f = 0 ↔ ∀ j ∈ s, f j = 0 := by
   simp only [← coe_to_submodule_inj, span_finset_coe, coe_zero, Submodule.span_eq_bot,
     Set.mem_image, Finset.mem_coe, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
 #align fractional_ideal.span_finset_eq_zero FractionalIdeal.spanFinset_eq_zero
+-/
 
+#print FractionalIdeal.spanFinset_ne_zero /-
 theorem spanFinset_ne_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f ≠ 0 ↔ ∃ j ∈ s, f j ≠ 0 := by simp
 #align fractional_ideal.span_finset_ne_zero FractionalIdeal.spanFinset_ne_zero
+-/
 
 open Submodule.IsPrincipal
 
-include loc
-
+#print FractionalIdeal.isFractional_span_singleton /-
 theorem isFractional_span_singleton (x : P) : IsFractional S (span R {x} : Submodule R P) :=
   let ⟨a, ha⟩ := exists_integer_multiple S x
   isFractional_span_iff.mpr ⟨a, a.2, fun x' hx' => (Set.mem_singleton_iff.mp hx').symm ▸ ha⟩
 #align fractional_ideal.is_fractional_span_singleton FractionalIdeal.isFractional_span_singleton
+-/
 
 variable (S)
 
@@ -1333,45 +1577,60 @@ theorem mem_spanSingleton_self (x : P) : x ∈ spanSingleton S x :=
 
 variable {S}
 
+#print FractionalIdeal.spanSingleton_le_iff_mem /-
 @[simp]
 theorem spanSingleton_le_iff_mem {x : P} {I : FractionalIdeal S P} :
     spanSingleton S x ≤ I ↔ x ∈ I := by
   rw [← coe_le_coe, coe_span_singleton, Submodule.span_singleton_le_iff_mem x ↑I, mem_coe]
 #align fractional_ideal.span_singleton_le_iff_mem FractionalIdeal.spanSingleton_le_iff_mem
+-/
 
+#print FractionalIdeal.spanSingleton_eq_spanSingleton /-
 theorem spanSingleton_eq_spanSingleton [NoZeroSMulDivisors R P] {x y : P} :
     spanSingleton S x = spanSingleton S y ↔ ∃ z : Rˣ, z • x = y :=
   by
   rw [← Submodule.span_singleton_eq_span_singleton, span_singleton, span_singleton]
   exact Subtype.mk_eq_mk
 #align fractional_ideal.span_singleton_eq_span_singleton FractionalIdeal.spanSingleton_eq_spanSingleton
+-/
 
+#print FractionalIdeal.eq_spanSingleton_of_principal /-
 theorem eq_spanSingleton_of_principal (I : FractionalIdeal S P) [IsPrincipal (I : Submodule R P)] :
     I = spanSingleton S (generator (I : Submodule R P)) := by rw [span_singleton];
   exact coe_to_submodule_injective (span_singleton_generator ↑I).symm
 #align fractional_ideal.eq_span_singleton_of_principal FractionalIdeal.eq_spanSingleton_of_principal
+-/
 
+#print FractionalIdeal.isPrincipal_iff /-
 theorem isPrincipal_iff (I : FractionalIdeal S P) :
     IsPrincipal (I : Submodule R P) ↔ ∃ x, I = spanSingleton S x :=
   ⟨fun h => ⟨@generator _ _ _ _ _ (↑I) h, @eq_spanSingleton_of_principal _ _ _ _ _ _ _ I h⟩,
     fun ⟨x, hx⟩ => { principal := ⟨x, trans (congr_arg _ hx) (coe_spanSingleton _ x)⟩ }⟩
 #align fractional_ideal.is_principal_iff FractionalIdeal.isPrincipal_iff
+-/
 
+#print FractionalIdeal.spanSingleton_zero /-
 @[simp]
 theorem spanSingleton_zero : spanSingleton S (0 : P) = 0 := by ext;
   simp [Submodule.mem_span_singleton, eq_comm]
 #align fractional_ideal.span_singleton_zero FractionalIdeal.spanSingleton_zero
+-/
 
+#print FractionalIdeal.spanSingleton_eq_zero_iff /-
 theorem spanSingleton_eq_zero_iff {y : P} : spanSingleton S y = 0 ↔ y = 0 :=
   ⟨fun h =>
     span_eq_bot.mp (by simpa using congr_arg Subtype.val h : span R {y} = ⊥) y (mem_singleton y),
     fun h => by simp [h]⟩
 #align fractional_ideal.span_singleton_eq_zero_iff FractionalIdeal.spanSingleton_eq_zero_iff
+-/
 
+#print FractionalIdeal.spanSingleton_ne_zero_iff /-
 theorem spanSingleton_ne_zero_iff {y : P} : spanSingleton S y ≠ 0 ↔ y ≠ 0 :=
   not_congr spanSingleton_eq_zero_iff
 #align fractional_ideal.span_singleton_ne_zero_iff FractionalIdeal.spanSingleton_ne_zero_iff
+-/
 
+#print FractionalIdeal.spanSingleton_one /-
 @[simp]
 theorem spanSingleton_one : spanSingleton S (1 : P) = 1 :=
   by
@@ -1380,7 +1639,9 @@ theorem spanSingleton_one : spanSingleton S (1 : P) = 1 :=
   intro x'
   rw [Algebra.smul_def, mul_one]
 #align fractional_ideal.span_singleton_one FractionalIdeal.spanSingleton_one
+-/
 
+#print FractionalIdeal.spanSingleton_mul_spanSingleton /-
 @[simp]
 theorem spanSingleton_mul_spanSingleton (x y : P) :
     spanSingleton S x * spanSingleton S y = spanSingleton S (x * y) :=
@@ -1388,7 +1649,9 @@ theorem spanSingleton_mul_spanSingleton (x y : P) :
   apply coe_to_submodule_injective
   simp only [coe_mul, coe_span_singleton, span_mul_span, singleton_mul_singleton]
 #align fractional_ideal.span_singleton_mul_span_singleton FractionalIdeal.spanSingleton_mul_spanSingleton
+-/
 
+#print FractionalIdeal.spanSingleton_pow /-
 @[simp]
 theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingleton S (x ^ n) :=
   by
@@ -1396,7 +1659,9 @@ theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingle
   · rw [pow_zero, pow_zero, span_singleton_one]
   · rw [pow_succ, hn, span_singleton_mul_span_singleton, pow_succ]
 #align fractional_ideal.span_singleton_pow FractionalIdeal.spanSingleton_pow
+-/
 
+#print FractionalIdeal.coeIdeal_span_singleton /-
 @[simp]
 theorem coeIdeal_span_singleton (x : R) :
     (↑(Ideal.span {x} : Ideal R) : FractionalIdeal S P) = spanSingleton S (algebraMap R P x) :=
@@ -1412,7 +1677,9 @@ theorem coeIdeal_span_singleton (x : R) :
     refine' ⟨y' * x, submodule.mem_span_singleton.mpr ⟨y', rfl⟩, _⟩
     rw [RingHom.map_mul, Algebra.smul_def]
 #align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coeIdeal_span_singleton
+-/
 
+#print FractionalIdeal.canonicalEquiv_spanSingleton /-
 @[simp]
 theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocalization S P']
     (x : P) :
@@ -1436,7 +1703,9 @@ theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocali
     use (mem_span_singleton _).mpr ⟨z, rfl⟩
     simp [IsLocalization.map_smul]
 #align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingleton
+-/
 
+#print FractionalIdeal.mem_singleton_mul /-
 theorem mem_singleton_mul {x y : P} {I : FractionalIdeal S P} :
     y ∈ spanSingleton S x * I ↔ ∃ y' ∈ I, y = x * y' :=
   by
@@ -1452,11 +1721,11 @@ theorem mem_singleton_mul {x y : P} {I : FractionalIdeal S P} :
   · rintro ⟨y', hy', rfl⟩
     exact mul_mem_mul ((mem_span_singleton S).mpr ⟨1, one_smul _ _⟩) hy'
 #align fractional_ideal.mem_singleton_mul FractionalIdeal.mem_singleton_mul
-
-omit loc
+-/
 
 variable (K)
 
+#print FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal /-
 theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈ R₁⁰) :
     spanSingleton R₁⁰ (IsLocalization.mk' K x ⟨y, hy⟩) * I = (J : FractionalIdeal R₁⁰ K) ↔
       Ideal.span {x} * I = Ideal.span {y} * J :=
@@ -1476,9 +1745,11 @@ theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈
     mul_comm (mk' _ _ _), ← IsLocalization.mk'_eq_mul_mk'_one, mul_comm (mk' _ _ _), ←
     IsLocalization.mk'_eq_mul_mk'_one, IsLocalization.mk'_self, span_singleton_one, one_mul]
 #align fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal
+-/
 
 variable {K}
 
+#print FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal /-
 theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
     spanSingleton R₁⁰ z * (I : FractionalIdeal R₁⁰ K) = J ↔
       Ideal.span {((IsLocalization.sec R₁⁰ z).1 : R₁)} * I =
@@ -1487,13 +1758,17 @@ theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
   erw [← mk'_mul_coe_ideal_eq_coe_ideal K (IsLocalization.sec R₁⁰ z).2.Prop,
     IsLocalization.mk'_sec K z]
 #align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal
+-/
 
 variable [IsDomain R₁]
 
+#print FractionalIdeal.one_div_spanSingleton /-
 theorem one_div_spanSingleton (x : K) : 1 / spanSingleton R₁⁰ x = spanSingleton R₁⁰ x⁻¹ :=
   if h : x = 0 then by simp [h] else (eq_one_div_of_mul_eq_one_right _ _ (by simp [h])).symm
 #align fractional_ideal.one_div_span_singleton FractionalIdeal.one_div_spanSingleton
+-/
 
+#print FractionalIdeal.div_spanSingleton /-
 @[simp]
 theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
     J / spanSingleton R₁⁰ d = spanSingleton R₁⁰ d⁻¹ * J :=
@@ -1513,7 +1788,9 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
       span_singleton_mul_span_singleton, inv_mul_cancel hd, span_singleton_one, mul_one]
     exact le_refl J
 #align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingleton
+-/
 
+#print FractionalIdeal.exists_eq_spanSingleton_mul /-
 theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
     ∃ (a : R₁) (aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI :=
   by
@@ -1537,6 +1814,7 @@ theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
     rw [Algebra.linearMap_apply] at hx' 
     rwa [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
 #align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mul
+-/
 
 #print FractionalIdeal.isPrincipal /-
 instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Algebra R K]
@@ -1552,14 +1830,15 @@ instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Alg
 #align fractional_ideal.is_principal FractionalIdeal.isPrincipal
 -/
 
-include loc
-
+#print FractionalIdeal.le_spanSingleton_mul_iff /-
 theorem le_spanSingleton_mul_iff {x : P} {I J : FractionalIdeal S P} :
     I ≤ spanSingleton S x * J ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI :=
   show (∀ {zI} (hzI : zI ∈ I), zI ∈ spanSingleton _ x * J) ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI by
     simp only [mem_singleton_mul, eq_comm]
 #align fractional_ideal.le_span_singleton_mul_iff FractionalIdeal.le_spanSingleton_mul_iff
+-/
 
+#print FractionalIdeal.spanSingleton_mul_le_iff /-
 theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
     spanSingleton _ x * I ≤ J ↔ ∀ z ∈ I, x * z ∈ J :=
   by
@@ -1571,11 +1850,14 @@ theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
     rw [Algebra.smul_mul_assoc]
     exact Submodule.smul_mem J.1 _ (h zI hzI)
 #align fractional_ideal.span_singleton_mul_le_iff FractionalIdeal.spanSingleton_mul_le_iff
+-/
 
+#print FractionalIdeal.eq_spanSingleton_mul /-
 theorem eq_spanSingleton_mul {x : P} {I J : FractionalIdeal S P} :
     I = spanSingleton _ x * J ↔ (∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI) ∧ ∀ z ∈ J, x * z ∈ I := by
   simp only [le_antisymm_iff, le_span_singleton_mul_iff, span_singleton_mul_le_iff]
 #align fractional_ideal.eq_span_singleton_mul FractionalIdeal.eq_spanSingleton_mul
+-/
 
 end PrincipalIdealRing
 
@@ -1585,16 +1867,21 @@ variable {K : Type _} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
 attribute [local instance] Classical.propDecidable
 
+#print FractionalIdeal.isNoetherian_zero /-
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
   isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by
     rw [coe_zero] at hI ; rw [le_bot_iff.mp hI]; exact fg_bot
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
+-/
 
+#print FractionalIdeal.isNoetherian_iff /-
 theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
     IsNoetherian R₁ I ↔ ∀ J ≤ I, (J : Submodule R₁ K).FG :=
   isNoetherian_submodule.trans ⟨fun h J hJ => h _ hJ, fun h J hJ => h ⟨J, isFractional_of_le hJ⟩ hJ⟩
 #align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iff
+-/
 
+#print FractionalIdeal.isNoetherian_coeIdeal /-
 theorem isNoetherian_coeIdeal [IsNoetherianRing R₁] (I : Ideal R₁) :
     IsNoetherian R₁ (I : FractionalIdeal R₁⁰ K) :=
   by
@@ -1603,11 +1890,11 @@ theorem isNoetherian_coeIdeal [IsNoetherianRing R₁] (I : Ideal R₁) :
   obtain ⟨J, rfl⟩ := le_one_iff_exists_coe_ideal.mp (le_trans hJ coe_ideal_le_one)
   exact (IsNoetherian.noetherian J).map _
 #align fractional_ideal.is_noetherian_coe_ideal FractionalIdeal.isNoetherian_coeIdeal
-
-include frac
+-/
 
 variable [IsDomain R₁]
 
+#print FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul /-
 theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdeal R₁⁰ K}
     (hI : IsNoetherian R₁ I) :
     IsNoetherian R₁ (spanSingleton R₁⁰ (algebraMap R₁ K x)⁻¹ * I : FractionalIdeal R₁⁰ K) :=
@@ -1627,7 +1914,9 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
     coe_mul, mul_assoc, span_singleton_mul_span_singleton, mul_inv_cancel h_gx, span_singleton_one,
     mul_one]
 #align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul
+-/
 
+#print FractionalIdeal.isNoetherian /-
 /-- Every fractional ideal of a noetherian integral domain is noetherian. -/
 theorem isNoetherian [IsNoetherianRing R₁] (I : FractionalIdeal R₁⁰ K) : IsNoetherian R₁ I :=
   by
@@ -1635,20 +1924,19 @@ theorem isNoetherian [IsNoetherianRing R₁] (I : FractionalIdeal R₁⁰ K) : I
   apply is_noetherian_span_singleton_inv_to_map_mul
   apply is_noetherian_coe_ideal
 #align fractional_ideal.is_noetherian FractionalIdeal.isNoetherian
+-/
 
 section Adjoin
 
-include loc
-
-omit frac
-
 variable {R P} (S) (x : P) (hx : IsIntegral R x)
 
+#print FractionalIdeal.isFractional_adjoin_integral /-
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Algebra.adjoin R ({x} : Set P)).toSubmodule :=
   isFractional_of_fg (FG_adjoin_singleton_of_integral x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
+-/
 
 #print FractionalIdeal.adjoinIntegral /-
 /-- `fractional_ideal.adjoin_integral (S : submonoid R) x hx` is `R[x]` as a fractional ideal,

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

@@ -987,7 +987,7 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
     ∃ (x : _) (_ : x ≠ (0 : R)), algebraMap R K x ∈ I :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

@@ -611,11 +611,13 @@ instance : CommSemiring (FractionalIdeal S P) :=
 
 variable (S P)
 
+#print FractionalIdeal.coeSubmoduleHom /-
 /-- `fractional_ideal.submodule.has_coe` as a bundled `ring_hom`. -/
 @[simps]
 def coeSubmoduleHom : FractionalIdeal S P →+* Submodule R P :=
   ⟨coe, coe_one, coe_mul, coe_zero, coe_add⟩
 #align fractional_ideal.coe_submodule_hom FractionalIdeal.coeSubmoduleHom
+-/
 
 variable {S P}
 
@@ -682,6 +684,7 @@ theorem one_le {I : FractionalIdeal S P} : 1 ≤ I ↔ (1 : P) ∈ I := by
 
 variable (S P)
 
+#print FractionalIdeal.coeIdealHom /-
 /-- `coe_ideal_hom (S : submonoid R) P` is `coe : ideal R → fractional_ideal S P` as a ring hom -/
 @[simps]
 def coeIdealHom : Ideal R →+* FractionalIdeal S P
@@ -692,6 +695,7 @@ def coeIdealHom : Ideal R →+* FractionalIdeal S P
   map_one' := by rw [Ideal.one_eq_top, coe_ideal_top]
   map_zero' := coeIdeal_bot
 #align fractional_ideal.coe_ideal_hom FractionalIdeal.coeIdealHom
+-/
 
 theorem coeIdeal_pow (I : Ideal R) (n : ℕ) : (↑(I ^ n) : FractionalIdeal S P) = I ^ n :=
   (coeIdealHom S P).map_pow _ n
@@ -878,9 +882,11 @@ theorem coeIdeal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
 
 variable {S}
 
+#print FractionalIdeal.fg_unit /-
 theorem fg_unit (I : (FractionalIdeal S P)ˣ) : FG (I : Submodule R P) :=
   Submodule.fg_unit <| Units.map (coeSubmoduleHom S P).toMonoidHom I
 #align fractional_ideal.fg_unit FractionalIdeal.fg_unit
+-/
 
 theorem fg_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : FG (I : Submodule R P) :=
   fg_unit h.Unit

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

@@ -485,7 +485,7 @@ theorem IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
   | 0, _ => by
     rw [zero_smul]
-    convert((0 : Ideal R) : FractionalIdeal S P).IsFractional
+    convert ((0 : Ideal R) : FractionalIdeal S P).IsFractional
     simp
   | n + 1, h => by
     rw [succ_nsmul]
@@ -653,7 +653,7 @@ theorem le_one_iff_exists_coeIdeal {J : FractionalIdeal S P} :
   by
   constructor
   · intro hJ
-    refine' ⟨⟨{ x : R | algebraMap R P x ∈ J }, _, _, _⟩, _⟩
+    refine' ⟨⟨{x : R | algebraMap R P x ∈ J}, _, _, _⟩, _⟩
     · intro a b ha hb
       rw [mem_set_of_eq, RingHom.map_add]
       exact J.val.add_mem ha hb
@@ -959,7 +959,7 @@ omit loc'
 theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ :=
   by
   rw [← canonical_equiv_trans_canonical_equiv S P P]
-  convert(canonical_equiv S P P).symm_trans_self
+  convert (canonical_equiv S P P).symm_trans_self
   exact (canonical_equiv_symm S P P).symm
 #align fractional_ideal.canonical_equiv_self FractionalIdeal.canonicalEquiv_self
 

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

@@ -594,7 +594,7 @@ theorem coe_pow (I : FractionalIdeal S P) (n : ℕ) : ↑(I ^ n) = (I ^ n : Subm
 protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop} {r : P}
     (hr : r ∈ I * J) (hm : ∀ i ∈ I, ∀ j ∈ J, C (i * j)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
   by
-  simp only [mul_def] at hr
+  simp only [mul_def] at hr 
   exact Submodule.mul_induction_on hr hm ha
 #align fractional_ideal.mul_induction_on FractionalIdeal.mul_induction_on
 
@@ -984,7 +984,7 @@ variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
-    ∃ (x : _)(_ : x ≠ (0 : R)), algebraMap R K x ∈ I :=
+    ∃ (x : _) (_ : x ≠ (0 : R)), algebraMap R K x ∈ I :=
   by
   obtain ⟨y, y_mem, y_not_mem⟩ :=
     SetLike.exists_of_lt (by simpa only using bot_lt_iff_ne_bot.mpr hI)
@@ -1143,7 +1143,7 @@ theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : Fra
   by_cases hI_nz : I = 0
   · rw [hI_nz, div_zero, MulZeroClass.mul_zero]; exact zero_le 0
   · rw [← coe_le_coe, coe_mul, coe_div hI_nz, coe_one]
-    rw [← coe_le_coe, coe_one] at hI
+    rw [← coe_le_coe, coe_one] at hI 
     exact Submodule.le_self_mul_one_div hI
 #align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_div
 
@@ -1498,7 +1498,7 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
   have h_spand : span_singleton R₁⁰ d ≠ 0 := mt span_singleton_eq_zero_iff.mp hd
   apply le_antisymm
   · intro x hx
-    rw [← mem_coe, coe_div h_spand, Submodule.mem_div_iff_forall_mul_mem] at hx
+    rw [← mem_coe, coe_div h_spand, Submodule.mem_div_iff_forall_mul_mem] at hx 
     specialize hx d (mem_span_singleton_self R₁⁰ d)
     have h_xd : x = d⁻¹ * (x * d) := by field_simp
     rw [← mem_coe, coe_mul, one_div_span_singleton, h_xd]
@@ -1509,7 +1509,7 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
 #align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingleton
 
 theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
-    ∃ (a : R₁)(aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI :=
+    ∃ (a : R₁) (aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI :=
   by
   obtain ⟨a_inv, nonzero, ha⟩ := I.is_fractional
   have nonzero := mem_non_zero_divisors_iff_ne_zero.mp nonzero
@@ -1521,14 +1521,14 @@ theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
       nonzero, ext fun x => Iff.trans ⟨_, _⟩ mem_singleton_mul.symm⟩
   · intro hx
     obtain ⟨x', hx'⟩ := ha x hx
-    rw [Algebra.smul_def] at hx'
+    rw [Algebra.smul_def] at hx' 
     refine' ⟨algebraMap R₁ K x', (mem_coe_ideal _).mpr ⟨x', mem_singleton_mul.mpr _, rfl⟩, _⟩
     · exact ⟨x, hx, hx'⟩
     · rw [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
   · rintro ⟨y, hy, rfl⟩
     obtain ⟨x', hx', rfl⟩ := (mem_coe_ideal _).mp hy
     obtain ⟨y', hy', hx'⟩ := mem_singleton_mul.mp hx'
-    rw [Algebra.linearMap_apply] at hx'
+    rw [Algebra.linearMap_apply] at hx' 
     rwa [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
 #align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mul
 
@@ -1539,7 +1539,7 @@ instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Alg
   obtain ⟨a, aI, -, ha⟩ := exists_eq_span_singleton_mul I
   use (algebraMap R K a)⁻¹ * algebraMap R K (generator aI)
   suffices I = span_singleton R⁰ ((algebraMap R K a)⁻¹ * algebraMap R K (generator aI)) by
-    rw [span_singleton] at this; exact congr_arg Subtype.val this
+    rw [span_singleton] at this ; exact congr_arg Subtype.val this
   conv_lhs => rw [ha, ← span_singleton_generator aI]
   rw [Ideal.submodule_span_eq, coe_ideal_span_singleton (generator aI),
     span_singleton_mul_span_singleton]
@@ -1580,8 +1580,8 @@ variable {K : Type _} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 attribute [local instance] Classical.propDecidable
 
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
-  isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by rw [coe_zero] at hI;
-    rw [le_bot_iff.mp hI]; exact fg_bot
+  isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by
+    rw [coe_zero] at hI ; rw [le_bot_iff.mp hI]; exact fg_bot
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 
 theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
@@ -1612,9 +1612,9 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
   have h_gx : algebraMap R₁ K x ≠ 0 :=
     mt ((injective_iff_map_eq_zero (algebraMap R₁ K)).mp (IsFractionRing.injective _ _) x) hx
   have h_spanx : span_singleton R₁⁰ (algebraMap R₁ K x) ≠ 0 := span_singleton_ne_zero_iff.mpr h_gx
-  rw [is_noetherian_iff] at hI⊢
+  rw [is_noetherian_iff] at hI ⊢
   intro J hJ
-  rw [← div_span_singleton, le_div_iff_mul_le h_spanx] at hJ
+  rw [← div_span_singleton, le_div_iff_mul_le h_spanx] at hJ 
   obtain ⟨s, hs⟩ := hI _ hJ
   use s * {(algebraMap R₁ K x)⁻¹}
   rw [Finset.coe_mul, Finset.coe_singleton, ← span_mul_span, hs, ← coe_span_singleton R₁⁰, ←

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

@@ -77,9 +77,9 @@ fractional ideal, fractional ideals, invertible ideal
 
 open IsLocalization
 
-open Pointwise
+open scoped Pointwise
 
-open nonZeroDivisors
+open scoped nonZeroDivisors
 
 section Defs
 
@@ -697,7 +697,7 @@ theorem coeIdeal_pow (I : Ideal R) (n : ℕ) : (↑(I ^ n) : FractionalIdeal S P
   (coeIdealHom S P).map_pow _ n
 #align fractional_ideal.coe_ideal_pow FractionalIdeal.coeIdeal_pow
 
-open BigOperators
+open scoped BigOperators
 
 theorem coeIdeal_finprod [IsLocalization S P] {α : Sort _} {f : α → Ideal R}
     (hS : S ≤ nonZeroDivisors R) :
@@ -1053,7 +1053,7 @@ is a field because `R` is a domain.
 -/
 
 
-open Classical
+open scoped Classical
 
 variable {R₁ : Type _} [CommRing R₁] {K : Type _} [Field K]
 
@@ -1254,7 +1254,7 @@ variable {R₁ : Type _} [CommRing R₁] {K : Type _} [Field K]
 
 variable [Algebra R₁ K] [IsFractionRing R₁ K]
 
-open Classical
+open scoped Classical
 
 variable (R₁)
 

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

@@ -132,12 +132,6 @@ not to be confused with `is_localization.coe_submodule : ideal R → submodule R
 instance : Coe (FractionalIdeal S P) (Submodule R P) :=
   ⟨fun I => I.val⟩
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional FractionalIdeal.isFractionalₓ'. -/
 protected theorem isFractional (I : FractionalIdeal S P) : IsFractional S (I : Submodule R P) :=
   I.Prop
 #align fractional_ideal.is_fractional FractionalIdeal.isFractional
@@ -149,23 +143,11 @@ instance : SetLike (FractionalIdeal S P) P
   coe I := ↑(I : Submodule R P)
   coe_injective' := SetLike.coe_injective.comp Subtype.coe_injective
 
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 @[simp]
 theorem mem_coe {I : FractionalIdeal S P} {x : P} : x ∈ (I : Submodule R P) ↔ x ∈ I :=
   Iff.rfl
 #align fractional_ideal.mem_coe FractionalIdeal.mem_coe
 
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 @[ext]
 theorem ext {I J : FractionalIdeal S P} : (∀ x, x ∈ I ↔ x ∈ J) → I = J :=
   SetLike.ext
@@ -179,43 +161,22 @@ protected def copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : Fract
 #align fractional_ideal.copy FractionalIdeal.copy
 -/
 
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 @[simp]
 theorem coe_copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : ↑(p.copy s hs) = s :=
   rfl
 #align fractional_ideal.coe_copy FractionalIdeal.coe_copy
 
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 theorem coe_eq (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : p.copy s hs = p :=
   SetLike.coe_injective hs
 #align fractional_ideal.coe_eq FractionalIdeal.coe_eq
 
 end SetLike
 
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 @[simp]
 theorem val_eq_coe (I : FractionalIdeal S P) : I.val = I :=
   rfl
 #align fractional_ideal.val_eq_coe FractionalIdeal.val_eq_coe
 
-/- warning: fractional_ideal.coe_mk -> FractionalIdeal.coe_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_mk FractionalIdeal.coe_mkₓ'. -/
 @[simp, norm_cast]
 theorem coe_mk (I : Submodule R P) (hI : IsFractional S I) :
     (Subtype.mk I hI : Submodule R P) = I :=
@@ -237,22 +198,10 @@ theorem coeToSubmodule_injective : Function.Injective (coe : FractionalIdeal S P
 #align fractional_ideal.coe_to_submodule_injective FractionalIdeal.coeToSubmodule_injective
 -/
 
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 theorem coeToSubmodule_inj {I J : FractionalIdeal S P} : (I : Submodule R P) = J ↔ I = J :=
   coeToSubmodule_injective.eq_iff
 #align fractional_ideal.coe_to_submodule_inj FractionalIdeal.coeToSubmodule_inj
 
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_inst_3)) (Submodule.one.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_of_le_one FractionalIdeal.isFractional_of_le_oneₓ'. -/
 theorem isFractional_of_le_one (I : Submodule R P) (h : I ≤ 1) : IsFractional S I :=
   by
   use 1, S.one_mem
@@ -262,12 +211,6 @@ theorem isFractional_of_le_one (I : Submodule R P) (h : I ≤ 1) : IsFractional
   exact Set.mem_range_self b'
 #align fractional_ideal.is_fractional_of_le_one FractionalIdeal.isFractional_of_le_one
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_of_le FractionalIdeal.isFractional_of_leₓ'. -/
 theorem isFractional_of_le {I : Submodule R P} {J : FractionalIdeal S P} (hIJ : I ≤ J) :
     IsFractional S I := by
   obtain ⟨a, a_mem, ha⟩ := J.is_fractional
@@ -290,12 +233,6 @@ instance : CoeTC (Ideal R) (FractionalIdeal S P) :=
     ⟨coeSubmodule P I,
       isFractional_of_le_one _ <| by simpa using coe_submodule_mono P (le_top : I ≤ ⊤)⟩⟩
 
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 @[simp, norm_cast]
 theorem coe_coeIdeal (I : Ideal R) :
     ((I : FractionalIdeal S P) : Submodule R P) = coeSubmodule P I :=
@@ -304,43 +241,22 @@ theorem coe_coeIdeal (I : Ideal R) :
 
 variable (S)
 
-/- warning: fractional_ideal.mem_coe_ideal -> FractionalIdeal.mem_coeIdeal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_coe_ideal FractionalIdeal.mem_coeIdealₓ'. -/
 @[simp]
 theorem mem_coeIdeal {x : P} {I : Ideal R} :
     x ∈ (I : FractionalIdeal S P) ↔ ∃ x', x' ∈ I ∧ algebraMap R P x' = x :=
   mem_coeSubmodule _ _
 #align fractional_ideal.mem_coe_ideal FractionalIdeal.mem_coeIdeal
 
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 theorem mem_coeIdeal_of_mem {x : R} {I : Ideal R} (hx : x ∈ I) :
     algebraMap R P x ∈ (I : FractionalIdeal S P) :=
   (mem_coeIdeal S).mpr ⟨x, hx, rfl⟩
 #align fractional_ideal.mem_coe_ideal_of_mem FractionalIdeal.mem_coeIdeal_of_mem
 
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 theorem coeIdeal_le_coeIdeal' [IsLocalization S P] (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
     (I : FractionalIdeal S P) ≤ J ↔ I ≤ J :=
   coeSubmodule_le_coeSubmodule h
 #align fractional_ideal.coe_ideal_le_coe_ideal' FractionalIdeal.coeIdeal_le_coeIdeal'
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_le_coe_ideal FractionalIdeal.coeIdeal_le_coeIdealₓ'. -/
 @[simp]
 theorem coeIdeal_le_coeIdeal (K : Type _) [CommRing K] [Algebra R K] [IsFractionRing R K]
     {I J : Ideal R} : (I : FractionalIdeal R⁰ K) ≤ J ↔ I ≤ J :=
@@ -350,12 +266,6 @@ theorem coeIdeal_le_coeIdeal (K : Type _) [CommRing K] [Algebra R K] [IsFraction
 instance : Zero (FractionalIdeal S P) :=
   ⟨(0 : Ideal R)⟩
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_zero_iff FractionalIdeal.mem_zero_iffₓ'. -/
 @[simp]
 theorem mem_zero_iff {x : P} : x ∈ (0 : FractionalIdeal S P) ↔ x = 0 :=
   ⟨fun ⟨x', x'_mem_zero, x'_eq_x⟩ =>
@@ -366,23 +276,11 @@ theorem mem_zero_iff {x : P} : x ∈ (0 : FractionalIdeal S P) ↔ x = 0 :=
 
 variable {S}
 
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 @[simp, norm_cast]
 theorem coe_zero : ↑(0 : FractionalIdeal S P) = (⊥ : Submodule R P) :=
   Submodule.ext fun _ => mem_zero_iff S
 #align fractional_ideal.coe_zero FractionalIdeal.coe_zero
 
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 @[simp, norm_cast]
 theorem coeIdeal_bot : ((⊥ : Ideal R) : FractionalIdeal S P) = 0 :=
   rfl
@@ -392,9 +290,6 @@ variable (P)
 
 include loc
 
-/- warning: fractional_ideal.exists_mem_to_map_eq -> FractionalIdeal.exists_mem_algebraMap_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_mem_to_map_eq FractionalIdeal.exists_mem_algebraMap_eqₓ'. -/
 @[simp]
 theorem exists_mem_algebraMap_eq {x : R} {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (∃ x', x' ∈ I ∧ algebraMap R P x' = algebraMap R P x) ↔ x ∈ I :=
@@ -403,46 +298,22 @@ theorem exists_mem_algebraMap_eq {x : R} {I : Ideal R} (h : S ≤ nonZeroDivisor
 
 variable {P}
 
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 theorem coeIdeal_injective' (h : S ≤ nonZeroDivisors R) :
     Function.Injective (coe : Ideal R → FractionalIdeal S P) := fun _ _ h' =>
   ((coeIdeal_le_coeIdeal' S h).mp h'.le).antisymm ((coeIdeal_le_coeIdeal' S h).mp h'.ge)
 #align fractional_ideal.coe_ideal_injective' FractionalIdeal.coeIdeal_injective'
 
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 theorem coeIdeal_inj' (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
     (I : FractionalIdeal S P) = J ↔ I = J :=
   (coeIdeal_injective' h).eq_iff
 #align fractional_ideal.coe_ideal_inj' FractionalIdeal.coeIdeal_inj'
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_eq_zero' FractionalIdeal.coeIdeal_eq_zero'ₓ'. -/
 @[simp]
 theorem coeIdeal_eq_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (I : FractionalIdeal S P) = 0 ↔ I = (⊥ : Ideal R) :=
   coeIdeal_inj' h
 #align fractional_ideal.coe_ideal_eq_zero' FractionalIdeal.coeIdeal_eq_zero'
 
-/- warning: fractional_ideal.coe_ideal_ne_zero' -> FractionalIdeal.coeIdeal_ne_zero' is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_ne_zero' FractionalIdeal.coeIdeal_ne_zero'ₓ'. -/
 theorem coeIdeal_ne_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (I : FractionalIdeal S P) ≠ 0 ↔ I ≠ (⊥ : Ideal R) :=
   not_iff_not.mpr <| coeIdeal_eq_zero' h
@@ -450,22 +321,10 @@ theorem coeIdeal_ne_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
 
 omit loc
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_to_submodule_eq_bot FractionalIdeal.coeToSubmodule_eq_botₓ'. -/
 theorem coeToSubmodule_eq_bot {I : FractionalIdeal S P} : (I : Submodule R P) = ⊥ ↔ I = 0 :=
   ⟨fun h => coeToSubmodule_injective (by simp [h]), fun h => by simp [h]⟩
 #align fractional_ideal.coe_to_submodule_eq_bot FractionalIdeal.coeToSubmodule_eq_bot
 
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 theorem coeToSubmodule_ne_bot {I : FractionalIdeal S P} : ↑I ≠ (⊥ : Submodule R P) ↔ I ≠ 0 :=
   not_iff_not.mpr coeToSubmodule_eq_bot
 #align fractional_ideal.coe_to_submodule_ne_bot FractionalIdeal.coeToSubmodule_ne_bot
@@ -478,55 +337,25 @@ instance : One (FractionalIdeal S P) :=
 
 variable (S)
 
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 @[simp, norm_cast]
 theorem coeIdeal_top : ((⊤ : Ideal R) : FractionalIdeal S P) = 1 :=
   rfl
 #align fractional_ideal.coe_ideal_top FractionalIdeal.coeIdeal_top
 
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 theorem mem_one_iff {x : P} : x ∈ (1 : FractionalIdeal S P) ↔ ∃ x' : R, algebraMap R P x' = x :=
   Iff.intro (fun ⟨x', _, h⟩ => ⟨x', h⟩) fun ⟨x', h⟩ => ⟨x', ⟨⟩, h⟩
 #align fractional_ideal.mem_one_iff FractionalIdeal.mem_one_iff
 
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 theorem coe_mem_one (x : R) : algebraMap R P x ∈ (1 : FractionalIdeal S P) :=
   (mem_one_iff S).mpr ⟨x, rfl⟩
 #align fractional_ideal.coe_mem_one FractionalIdeal.coe_mem_one
 
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 theorem one_mem_one : (1 : P) ∈ (1 : FractionalIdeal S P) :=
   (mem_one_iff S).mpr ⟨1, RingHom.map_one _⟩
 #align fractional_ideal.one_mem_one FractionalIdeal.one_mem_one
 
 variable {S}
 
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 /-- `(1 : fractional_ideal S P)` is defined as the R-submodule `f(R) ≤ P`.
 
 However, this is not definitionally equal to `1 : submodule R P`,
@@ -535,12 +364,6 @@ theorem coe_one_eq_coeSubmodule_top : ↑(1 : FractionalIdeal S P) = coeSubmodul
   rfl
 #align fractional_ideal.coe_one_eq_coe_submodule_top FractionalIdeal.coe_one_eq_coeSubmodule_top
 
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 @[simp, norm_cast]
 theorem coe_one : (↑(1 : FractionalIdeal S P) : Submodule R P) = 1 := by
   rw [coe_one_eq_coe_submodule_top, coe_submodule_top]
@@ -556,21 +379,12 @@ and ports the lattice structure on submodules to fractional ideals.
 -/
 
 
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 @[simp]
 theorem coe_le_coe {I J : FractionalIdeal S P} :
     (I : Submodule R P) ≤ (J : Submodule R P) ↔ I ≤ J :=
   Iff.rfl
 #align fractional_ideal.coe_le_coe FractionalIdeal.coe_le_coe
 
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 theorem zero_le (I : FractionalIdeal S P) : 0 ≤ I :=
   by
   intro x hx
@@ -578,57 +392,27 @@ theorem zero_le (I : FractionalIdeal S P) : 0 ≤ I :=
   simpa using hx
 #align fractional_ideal.zero_le FractionalIdeal.zero_le
 
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 instance orderBot : OrderBot (FractionalIdeal S P)
     where
   bot := 0
   bot_le := zero_le
 #align fractional_ideal.order_bot FractionalIdeal.orderBot
 
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 @[simp]
 theorem bot_eq_zero : (⊥ : FractionalIdeal S P) = 0 :=
   rfl
 #align fractional_ideal.bot_eq_zero FractionalIdeal.bot_eq_zero
 
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 @[simp]
 theorem le_zero_iff {I : FractionalIdeal S P} : I ≤ 0 ↔ I = 0 :=
   le_bot_iff
 #align fractional_ideal.le_zero_iff FractionalIdeal.le_zero_iff
 
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 theorem eq_zero_iff {I : FractionalIdeal S P} : I = 0 ↔ ∀ x ∈ I, x = (0 : P) :=
   ⟨fun h x hx => by simpa [h, mem_zero_iff] using hx, fun h =>
     le_bot_iff.mp fun x hx => (mem_zero_iff S).mpr (h x hx)⟩
 #align fractional_ideal.eq_zero_iff FractionalIdeal.eq_zero_iff
 
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 theorem IsFractional.sup {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I ⊔ J)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
@@ -643,12 +427,6 @@ theorem IsFractional.sup {I J : Submodule R P} :
         exact is_integer_smul (hJ bJ hbJ)⟩
 #align is_fractional.sup IsFractional.sup
 
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-Case conversion may be inaccurate. Consider using '#align is_fractional.inf_right IsFractional.inf_rightₓ'. -/
 theorem IsFractional.inf_right {I : Submodule R P} : IsFractional S I → ∀ J, IsFractional S (I ⊓ J)
   | ⟨aI, haI, hI⟩, J =>
     ⟨aI, haI, fun b hb => by
@@ -659,9 +437,6 @@ theorem IsFractional.inf_right {I : Submodule R P} : IsFractional S I → ∀ J,
 instance : Inf (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊓ J, I.IsFractional.inf_right J⟩⟩
 
-/- warning: fractional_ideal.coe_inf -> FractionalIdeal.coe_inf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_inf FractionalIdeal.coe_infₓ'. -/
 @[simp, norm_cast]
 theorem coe_inf (I J : FractionalIdeal S P) : ↑(I ⊓ J) = (I ⊓ J : Submodule R P) :=
   rfl
@@ -670,9 +445,6 @@ theorem coe_inf (I J : FractionalIdeal S P) : ↑(I ⊓ J) = (I ⊓ J : Submodul
 instance : Sup (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊔ J, I.IsFractional.sup J.IsFractional⟩⟩
 
-/- warning: fractional_ideal.coe_sup -> FractionalIdeal.coe_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_sup FractionalIdeal.coe_supₓ'. -/
 @[norm_cast]
 theorem coe_sup (I J : FractionalIdeal S P) : ↑(I ⊔ J) = (I ⊔ J : Submodule R P) :=
   rfl
@@ -694,39 +466,21 @@ section Semiring
 instance : Add (FractionalIdeal S P) :=
   ⟨(· ⊔ ·)⟩
 
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 @[simp]
 theorem sup_eq_add (I J : FractionalIdeal S P) : I ⊔ J = I + J :=
   rfl
 #align fractional_ideal.sup_eq_add FractionalIdeal.sup_eq_add
 
-/- warning: fractional_ideal.coe_add -> FractionalIdeal.coe_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_add FractionalIdeal.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add (I J : FractionalIdeal S P) : (↑(I + J) : Submodule R P) = I + J :=
   rfl
 #align fractional_ideal.coe_add FractionalIdeal.coe_add
 
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 @[simp, norm_cast]
 theorem coeIdeal_sup (I J : Ideal R) : ↑(I ⊔ J) = (I + J : FractionalIdeal S P) :=
   coeToSubmodule_injective <| coeSubmodule_sup _ _ _
 #align fractional_ideal.coe_ideal_sup FractionalIdeal.coeIdeal_sup
 
-/- warning: is_fractional.nsmul -> IsFractional.nsmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fractional.nsmul IsFractional.nsmulₓ'. -/
 theorem IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
   | 0, _ => by
@@ -740,20 +494,11 @@ theorem IsFractional.nsmul {I : Submodule R P} :
 
 instance : SMul ℕ (FractionalIdeal S P) where smul n I := ⟨n • I, I.IsFractional.nsmul n⟩
 
-/- warning: fractional_ideal.coe_nsmul -> FractionalIdeal.coe_nsmul is a dubious translation:
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 @[norm_cast]
 theorem coe_nsmul (n : ℕ) (I : FractionalIdeal S P) : (↑(n • I) : Submodule R P) = n • I :=
   rfl
 #align fractional_ideal.coe_nsmul FractionalIdeal.coe_nsmul
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_fractional.mul IsFractional.mulₓ'. -/
 theorem IsFractional.mul {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I * J : Submodule R P)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
@@ -770,12 +515,6 @@ theorem IsFractional.mul {I J : Submodule R P} :
         apply is_integer_add hx hy⟩
 #align is_fractional.mul IsFractional.mul
 
-/- warning: is_fractional.pow -> IsFractional.pow is a dubious translation:
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-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)}, (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) -> (forall (n : Nat), IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HPow.hPow.{u1, 0, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) Nat (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHPow.{u1, 0} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) Nat (Monoid.Pow.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) I n))
-Case conversion may be inaccurate. Consider using '#align is_fractional.pow IsFractional.powₓ'. -/
 theorem IsFractional.pow {I : Submodule R P} (h : IsFractional S I) :
     ∀ n : ℕ, IsFractional S (I ^ n : Submodule R P)
   | 0 => isFractional_of_le_one _ (pow_zero _).le
@@ -800,38 +539,20 @@ irreducible_def mul (I J : FractionalIdeal S P) : FractionalIdeal S P :=
 instance : Mul (FractionalIdeal S P) :=
   ⟨fun I J => mul I J⟩
 
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 @[simp]
 theorem mul_eq_mul (I J : FractionalIdeal S P) : mul I J = I * J :=
   rfl
 #align fractional_ideal.mul_eq_mul FractionalIdeal.mul_eq_mul
 
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 theorem mul_def (I J : FractionalIdeal S P) : I * J = ⟨I * J, I.IsFractional.mul J.IsFractional⟩ :=
   by simp only [← mul_eq_mul, mul]
 #align fractional_ideal.mul_def FractionalIdeal.mul_def
 
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 @[simp, norm_cast]
 theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I * J := by
   simp only [mul_def]; rfl
 #align fractional_ideal.coe_mul FractionalIdeal.coe_mul
 
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 @[simp, norm_cast]
 theorem coeIdeal_mul (I J : Ideal R) : (↑(I * J) : FractionalIdeal S P) = I * J :=
   by
@@ -839,12 +560,6 @@ theorem coeIdeal_mul (I J : Ideal R) : (↑(I * J) : FractionalIdeal S P) = I *
   exact coe_to_submodule_injective (coe_submodule_mul _ _ _)
 #align fractional_ideal.coe_ideal_mul FractionalIdeal.coeIdeal_mul
 
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 theorem mul_left_mono (I : FractionalIdeal S P) : Monotone ((· * ·) I) :=
   by
   intro J J' h
@@ -852,12 +567,6 @@ theorem mul_left_mono (I : FractionalIdeal S P) : Monotone ((· * ·) I) :=
   exact mul_le.mpr fun x hx y hy => mul_mem_mul hx (h hy)
 #align fractional_ideal.mul_left_mono FractionalIdeal.mul_left_mono
 
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 theorem mul_right_mono (I : FractionalIdeal S P) : Monotone fun J => J * I :=
   by
   intro J J' h
@@ -865,22 +574,10 @@ theorem mul_right_mono (I : FractionalIdeal S P) : Monotone fun J => J * I :=
   exact mul_le.mpr fun x hx y hy => mul_mem_mul (h hx) hy
 #align fractional_ideal.mul_right_mono FractionalIdeal.mul_right_mono
 
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 theorem mul_mem_mul {I J : FractionalIdeal S P} {i j : P} (hi : i ∈ I) (hj : j ∈ J) :
     i * j ∈ I * J := by simp only [mul_def]; exact Submodule.mul_mem_mul hi hj
 #align fractional_ideal.mul_mem_mul FractionalIdeal.mul_mem_mul
 
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 theorem mul_le {I J K : FractionalIdeal S P} : I * J ≤ K ↔ ∀ i ∈ I, ∀ j ∈ J, i * j ∈ K := by
   simp only [mul_def]; exact Submodule.mul_le
 #align fractional_ideal.mul_le FractionalIdeal.mul_le
@@ -888,20 +585,11 @@ theorem mul_le {I J K : FractionalIdeal S P} : I * J ≤ K ↔ ∀ i ∈ I, ∀
 instance : Pow (FractionalIdeal S P) ℕ :=
   ⟨fun I n => ⟨I ^ n, I.IsFractional.pow n⟩⟩
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_pow FractionalIdeal.coe_powₓ'. -/
 @[simp, norm_cast]
 theorem coe_pow (I : FractionalIdeal S P) (n : ℕ) : ↑(I ^ n) = (I ^ n : Submodule R P) :=
   rfl
 #align fractional_ideal.coe_pow FractionalIdeal.coe_pow
 
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 @[elab_as_elim]
 protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop} {r : P}
     (hr : r ∈ I * J) (hm : ∀ i ∈ I, ∀ j ∈ J, C (i * j)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
@@ -913,9 +601,6 @@ protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop}
 instance : NatCast (FractionalIdeal S P) :=
   ⟨Nat.unaryCast⟩
 
-/- warning: fractional_ideal.coe_nat_cast -> FractionalIdeal.coe_nat_cast is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_castₓ'. -/
 theorem coe_nat_cast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
   show ↑n.unaryCast = ↑n by induction n <;> simp [*, Nat.unaryCast]
 #align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_cast
@@ -926,12 +611,6 @@ instance : CommSemiring (FractionalIdeal S P) :=
 
 variable (S P)
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_submodule_hom FractionalIdeal.coeSubmoduleHomₓ'. -/
 /-- `fractional_ideal.submodule.has_coe` as a bundled `ring_hom`. -/
 @[simps]
 def coeSubmoduleHom : FractionalIdeal S P →+* Submodule R P :=
@@ -942,69 +621,33 @@ variable {S P}
 
 section Order
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.add_le_add_left FractionalIdeal.add_le_add_leftₓ'. -/
 theorem add_le_add_left {I J : FractionalIdeal S P} (hIJ : I ≤ J) (J' : FractionalIdeal S P) :
     J' + I ≤ J' + J :=
   sup_le_sup_left hIJ J'
 #align fractional_ideal.add_le_add_left FractionalIdeal.add_le_add_left
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_le_mul_left FractionalIdeal.mul_le_mul_leftₓ'. -/
 theorem mul_le_mul_left {I J : FractionalIdeal S P} (hIJ : I ≤ J) (J' : FractionalIdeal S P) :
     J' * I ≤ J' * J :=
   mul_le.mpr fun k hk j hj => mul_mem_mul hk (hIJ hj)
 #align fractional_ideal.mul_le_mul_left FractionalIdeal.mul_le_mul_left
 
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 theorem le_self_mul_self {I : FractionalIdeal S P} (hI : 1 ≤ I) : I ≤ I * I :=
   by
   convert mul_left_mono I hI
   exact (mul_one I).symm
 #align fractional_ideal.le_self_mul_self FractionalIdeal.le_self_mul_self
 
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 theorem mul_self_le_self {I : FractionalIdeal S P} (hI : I ≤ 1) : I * I ≤ I :=
   by
   convert mul_left_mono I hI
   exact (mul_one I).symm
 #align fractional_ideal.mul_self_le_self FractionalIdeal.mul_self_le_self
 
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 theorem coeIdeal_le_one {I : Ideal R} : (I : FractionalIdeal S P) ≤ 1 := fun x hx =>
   let ⟨y, _, hy⟩ := (mem_coeIdeal S).mp hx
   (mem_one_iff S).mpr ⟨y, hy⟩
 #align fractional_ideal.coe_ideal_le_one FractionalIdeal.coeIdeal_le_one
 
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 theorem le_one_iff_exists_coeIdeal {J : FractionalIdeal S P} :
     J ≤ (1 : FractionalIdeal S P) ↔ ∃ I : Ideal R, ↑I = J :=
   by
@@ -1032,12 +675,6 @@ theorem le_one_iff_exists_coeIdeal {J : FractionalIdeal S P} :
     apply coe_ideal_le_one
 #align fractional_ideal.le_one_iff_exists_coe_ideal FractionalIdeal.le_one_iff_exists_coeIdeal
 
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 @[simp]
 theorem one_le {I : FractionalIdeal S P} : 1 ≤ I ↔ (1 : P) ∈ I := by
   rw [← coe_le_coe, coe_one, Submodule.one_le, mem_coe]
@@ -1045,12 +682,6 @@ theorem one_le {I : FractionalIdeal S P} : 1 ≤ I ↔ (1 : P) ∈ I := by
 
 variable (S P)
 
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 /-- `coe_ideal_hom (S : submonoid R) P` is `coe : ideal R → fractional_ideal S P` as a ring hom -/
 @[simps]
 def coeIdealHom : Ideal R →+* FractionalIdeal S P
@@ -1062,24 +693,12 @@ def coeIdealHom : Ideal R →+* FractionalIdeal S P
   map_zero' := coeIdeal_bot
 #align fractional_ideal.coe_ideal_hom FractionalIdeal.coeIdealHom
 
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 theorem coeIdeal_pow (I : Ideal R) (n : ℕ) : (↑(I ^ n) : FractionalIdeal S P) = I ^ n :=
   (coeIdealHom S P).map_pow _ n
 #align fractional_ideal.coe_ideal_pow FractionalIdeal.coeIdeal_pow
 
 open BigOperators
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_finprod FractionalIdeal.coeIdeal_finprodₓ'. -/
 theorem coeIdeal_finprod [IsLocalization S P] {α : Sort _} {f : α → Ideal R}
     (hS : S ≤ nonZeroDivisors R) :
     ((∏ᶠ a : α, f a : Ideal R) : FractionalIdeal S P) = ∏ᶠ a : α, (f a : FractionalIdeal S P) :=
@@ -1092,12 +711,6 @@ variable {P' : Type _} [CommRing P'] [Algebra R P'] [loc' : IsLocalization S P']
 
 variable {P'' : Type _} [CommRing P''] [Algebra R P''] [loc'' : IsLocalization S P'']
 
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(CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 g) I))
-Case conversion may be inaccurate. Consider using '#align is_fractional.map IsFractional.mapₓ'. -/
 theorem IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
     IsFractional S I → IsFractional S (Submodule.map g.toLinearMap I)
   | ⟨a, a_nonzero, hI⟩ =>
@@ -1116,18 +729,12 @@ def map (g : P →ₐ[R] P') : FractionalIdeal S P → FractionalIdeal S P' := f
 #align fractional_ideal.map FractionalIdeal.map
 -/
 
-/- warning: fractional_ideal.coe_map -> FractionalIdeal.coe_map is a dubious translation:
-<too large>
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 @[simp, norm_cast]
 theorem coe_map (g : P →ₐ[R] P') (I : FractionalIdeal S P) :
     ↑(map g I) = Submodule.map g.toLinearMap I :=
   rfl
 #align fractional_ideal.coe_map FractionalIdeal.coe_map
 
-/- warning: fractional_ideal.mem_map -> FractionalIdeal.mem_map is a dubious translation:
-<too large>
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 @[simp]
 theorem mem_map {I : FractionalIdeal S P} {g : P →ₐ[R] P'} {y : P'} :
     y ∈ I.map g ↔ ∃ x, x ∈ I ∧ g x = y :=
@@ -1143,20 +750,11 @@ theorem map_id : I.map (AlgHom.id _ _) = I :=
 #align fractional_ideal.map_id FractionalIdeal.map_id
 -/
 
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-<too large>
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 @[simp]
 theorem map_comp (g' : P' →ₐ[R] P'') : I.map (g'.comp g) = (I.map g).map g' :=
   coeToSubmodule_injective (Submodule.map_comp g.toLinearMap g'.toLinearMap I)
 #align fractional_ideal.map_comp FractionalIdeal.map_comp
 
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 @[simp, norm_cast]
 theorem map_coeIdeal (I : Ideal R) : (I : FractionalIdeal S P).map g = I :=
   by
@@ -1169,45 +767,21 @@ theorem map_coeIdeal (I : Ideal R) : (I : FractionalIdeal S P).map g = I :=
     exact ⟨_, ⟨y, hy, rfl⟩, g.commutes y⟩
 #align fractional_ideal.map_coe_ideal FractionalIdeal.map_coeIdeal
 
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 @[simp]
 theorem map_one : (1 : FractionalIdeal S P).map g = 1 :=
   map_coeIdeal g ⊤
 #align fractional_ideal.map_one FractionalIdeal.map_one
 
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 @[simp]
 theorem map_zero : (0 : FractionalIdeal S P).map g = 0 :=
   map_coeIdeal g 0
 #align fractional_ideal.map_zero FractionalIdeal.map_zero
 
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 @[simp]
 theorem map_add : (I + J).map g = I.map g + J.map g :=
   coeToSubmodule_injective (Submodule.map_sup _ _ _)
 #align fractional_ideal.map_add FractionalIdeal.map_add
 
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 @[simp]
 theorem map_mul : (I * J).map g = I.map g * J.map g :=
   by
@@ -1215,45 +789,27 @@ theorem map_mul : (I * J).map g = I.map g * J.map g :=
   exact coe_to_submodule_injective (Submodule.map_mul _ _ _)
 #align fractional_ideal.map_mul FractionalIdeal.map_mul
 
-/- warning: fractional_ideal.map_map_symm -> FractionalIdeal.map_map_symm is a dubious translation:
-<too large>
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 @[simp]
 theorem map_map_symm (g : P ≃ₐ[R] P') : (I.map (g : P →ₐ[R] P')).map (g.symm : P' →ₐ[R] P) = I := by
   rw [← map_comp, g.symm_comp, map_id]
 #align fractional_ideal.map_map_symm FractionalIdeal.map_map_symm
 
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 @[simp]
 theorem map_symm_map (I : FractionalIdeal S P') (g : P ≃ₐ[R] P') :
     (I.map (g.symm : P' →ₐ[R] P)).map (g : P →ₐ[R] P') = I := by
   rw [← map_comp, g.comp_symm, map_id]
 #align fractional_ideal.map_symm_map FractionalIdeal.map_symm_map
 
-/- warning: fractional_ideal.map_mem_map -> FractionalIdeal.map_mem_map is a dubious translation:
-<too large>
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 theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I : FractionalIdeal S P} :
     f x ∈ map f I ↔ x ∈ I :=
   mem_map.trans ⟨fun ⟨x', hx', x'_eq⟩ => h x'_eq ▸ hx', fun h => ⟨x, h, rfl⟩⟩
 #align fractional_ideal.map_mem_map FractionalIdeal.map_mem_map
 
-/- warning: fractional_ideal.map_injective -> FractionalIdeal.map_injective is a dubious translation:
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 theorem map_injective (f : P →ₐ[R] P') (h : Function.Injective f) :
     Function.Injective (map f : FractionalIdeal S P → FractionalIdeal S P') := fun I J hIJ =>
   ext fun x => (map_mem_map h).symm.trans (hIJ.symm ▸ map_mem_map h)
 #align fractional_ideal.map_injective FractionalIdeal.map_injective
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_equiv FractionalIdeal.mapEquivₓ'. -/
 /-- If `g` is an equivalence, `map g` is an isomorphism -/
 def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S P'
     where
@@ -1265,49 +821,28 @@ def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S
   right_inv I := by rw [← map_comp, AlgEquiv.comp_symm, map_id]
 #align fractional_ideal.map_equiv FractionalIdeal.mapEquiv
 
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 @[simp]
 theorem coeFun_mapEquiv (g : P ≃ₐ[R] P') :
     (mapEquiv g : FractionalIdeal S P → FractionalIdeal S P') = map g :=
   rfl
 #align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coeFun_mapEquiv
 
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 @[simp]
 theorem mapEquiv_apply (g : P ≃ₐ[R] P') (I : FractionalIdeal S P) : mapEquiv g I = map (↑g) I :=
   rfl
 #align fractional_ideal.map_equiv_apply FractionalIdeal.mapEquiv_apply
 
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 @[simp]
 theorem mapEquiv_symm (g : P ≃ₐ[R] P') :
     ((mapEquiv g).symm : FractionalIdeal S P' ≃+* _) = mapEquiv g.symm :=
   rfl
 #align fractional_ideal.map_equiv_symm FractionalIdeal.mapEquiv_symm
 
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 @[simp]
 theorem mapEquiv_refl : mapEquiv AlgEquiv.refl = RingEquiv.refl (FractionalIdeal S P) :=
   RingEquiv.ext fun x => by simp
 #align fractional_ideal.map_equiv_refl FractionalIdeal.mapEquiv_refl
 
-/- warning: fractional_ideal.is_fractional_span_iff -> FractionalIdeal.isFractional_span_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_span_iff FractionalIdeal.isFractional_span_iffₓ'. -/
 theorem isFractional_span_iff {s : Set P} :
     IsFractional S (span R s) ↔ ∃ a ∈ S, ∀ b : P, b ∈ s → IsInteger R (a • b) :=
   ⟨fun ⟨a, a_mem, h⟩ => ⟨a, a_mem, fun b hb => h b (subset_span hb)⟩, fun ⟨a, a_mem, h⟩ =>
@@ -1319,12 +854,6 @@ theorem isFractional_span_iff {s : Set P} :
 
 include loc
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fgₓ'. -/
 theorem isFractional_of_fg {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
   by
   rcases hI with ⟨I, rfl⟩
@@ -1335,9 +864,6 @@ theorem isFractional_of_fg {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
 
 omit loc
 
-/- warning: fractional_ideal.mem_span_mul_finite_of_mem_mul -> FractionalIdeal.mem_span_mul_finite_of_mem_mul is a dubious translation:
-<too large>
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 theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx : x ∈ I * J) :
     ∃ T T' : Finset P, (T : Set P) ⊆ I ∧ (T' : Set P) ⊆ J ∧ x ∈ span R (T * T' : Set P) :=
   Submodule.mem_span_mul_finite_of_mem_mul (by simpa using mem_coe.mpr hx)
@@ -1345,12 +871,6 @@ theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx :
 
 variable (S)
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_fg FractionalIdeal.coeIdeal_fgₓ'. -/
 theorem coeIdeal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
     FG ((I : FractionalIdeal S P) : Submodule R P) ↔ I.FG :=
   coeSubmodule_fg _ inj _
@@ -1358,32 +878,14 @@ theorem coeIdeal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
 
 variable {S}
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.fg_unit FractionalIdeal.fg_unitₓ'. -/
 theorem fg_unit (I : (FractionalIdeal S P)ˣ) : FG (I : Submodule R P) :=
   Submodule.fg_unit <| Units.map (coeSubmoduleHom S P).toMonoidHom I
 #align fractional_ideal.fg_unit FractionalIdeal.fg_unit
 
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 theorem fg_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : FG (I : Submodule R P) :=
   fg_unit h.Unit
 #align fractional_ideal.fg_of_is_unit FractionalIdeal.fg_of_isUnit
 
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-Case conversion may be inaccurate. Consider using '#align ideal.fg_of_is_unit Ideal.fg_of_isUnitₓ'. -/
 theorem Ideal.fg_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
     (h : IsUnit (I : FractionalIdeal S P)) : I.FG := by rw [← coe_ideal_fg S inj I];
   exact fg_of_is_unit I h
@@ -1393,12 +895,6 @@ variable (S P P')
 
 include loc loc'
 
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 /-- `canonical_equiv f f'` is the canonical equivalence between the fractional
 ideals in `P` and in `P'` -/
 noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* FractionalIdeal S P' :=
@@ -1409,9 +905,6 @@ noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* Fractio
       commutes' := fun r => ringEquivOfRingEquiv_eq _ _ }
 #align fractional_ideal.canonical_equiv FractionalIdeal.canonicalEquiv
 
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-<too large>
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 @[simp]
 theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
     x ∈ canonicalEquiv S P P' I ↔
@@ -1424,12 +917,6 @@ theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
   exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
 #align fractional_ideal.mem_canonical_equiv_apply FractionalIdeal.mem_canonicalEquiv_apply
 
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 @[simp]
 theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P' P :=
   RingEquiv.ext fun I =>
@@ -1440,16 +927,10 @@ theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P'
       exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
 #align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symm
 
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 theorem canonicalEquiv_flip (I) : canonicalEquiv S P P' (canonicalEquiv S P' P I) = I := by
   rw [← canonical_equiv_symm, RingEquiv.symm_apply_apply]
 #align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flip
 
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 @[simp]
 theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] (I : FractionalIdeal S P) :
@@ -1461,18 +942,12 @@ theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P
   rfl
 #align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquiv
 
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 theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] :
     (canonicalEquiv S P P').trans (canonicalEquiv S P' P'') = canonicalEquiv S P P'' :=
   RingEquiv.ext (canonicalEquiv_canonicalEquiv S P P' P'')
 #align fractional_ideal.canonical_equiv_trans_canonical_equiv FractionalIdeal.canonicalEquiv_trans_canonicalEquiv
 
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 @[simp]
 theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I := by ext;
   simp [IsLocalization.map_eq]
@@ -1480,12 +955,6 @@ theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I := b
 
 omit loc'
 
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 @[simp]
 theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ :=
   by
@@ -1512,9 +981,6 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
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-<too large>
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
@@ -1531,12 +997,6 @@ theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
     exact smul_mem _ _ y_mem
 #align fractional_ideal.exists_ne_zero_mem_is_integer FractionalIdeal.exists_ne_zero_mem_isInteger
 
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 theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 :=
   by
   obtain ⟨x, x_ne_zero, hx⟩ := exists_ne_zero_mem_is_integer hI
@@ -1545,73 +1005,34 @@ theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 :=
   exact ⟨algebraMap R K x, hx, h.commutes x⟩
 #align fractional_ideal.map_ne_zero FractionalIdeal.map_ne_zero
 
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-<too large>
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 @[simp]
 theorem map_eq_zero_iff [Nontrivial R] : I.map h = 0 ↔ I = 0 :=
   ⟨imp_of_not_imp_not _ _ (map_ne_zero _), fun hI => hI.symm ▸ map_zero h⟩
 #align fractional_ideal.map_eq_zero_iff FractionalIdeal.map_eq_zero_iff
 
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 theorem coeIdeal_injective : Function.Injective (coe : Ideal R → FractionalIdeal R⁰ K) :=
   coeIdeal_injective' le_rfl
 #align fractional_ideal.coe_ideal_injective FractionalIdeal.coeIdeal_injective
 
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 theorem coeIdeal_inj {I J : Ideal R} :
     (I : FractionalIdeal R⁰ K) = (J : FractionalIdeal R⁰ K) ↔ I = J :=
   coeIdeal_inj' le_rfl
 #align fractional_ideal.coe_ideal_inj FractionalIdeal.coeIdeal_inj
 
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 @[simp]
 theorem coeIdeal_eq_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 0 ↔ I = ⊥ :=
   coeIdeal_eq_zero' le_rfl
 #align fractional_ideal.coe_ideal_eq_zero FractionalIdeal.coeIdeal_eq_zero
 
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 theorem coeIdeal_ne_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 0 ↔ I ≠ ⊥ :=
   coeIdeal_ne_zero' le_rfl
 #align fractional_ideal.coe_ideal_ne_zero FractionalIdeal.coeIdeal_ne_zero
 
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 @[simp]
 theorem coeIdeal_eq_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 1 ↔ I = 1 := by
   simpa only [Ideal.one_eq_top] using coe_ideal_inj
 #align fractional_ideal.coe_ideal_eq_one FractionalIdeal.coeIdeal_eq_one
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coeIdeal_ne_oneₓ'. -/
 theorem coeIdeal_ne_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 1 ↔ I ≠ 1 :=
   not_iff_not.mpr coeIdeal_eq_one
 #align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coeIdeal_ne_one
@@ -1644,12 +1065,6 @@ instance : Nontrivial (FractionalIdeal R₁⁰ K) :=
         simpa only [h] using coe_mem_one R₁⁰ 1
       one_ne_zero ((mem_zero_iff _).mp this)⟩⟩
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.ne_zero_of_mul_eq_one FractionalIdeal.ne_zero_of_mul_eq_oneₓ'. -/
 theorem ne_zero_of_mul_eq_one (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : I ≠ 0 := fun hI =>
   zero_ne_one' (FractionalIdeal R₁⁰ K) (by convert h; simp [hI])
 #align fractional_ideal.ne_zero_of_mul_eq_one FractionalIdeal.ne_zero_of_mul_eq_one
@@ -1658,9 +1073,6 @@ variable [IsDomain R₁]
 
 include frac
 
-/- warning: is_fractional.div_of_nonzero -> IsFractional.div_of_nonzero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fractional.div_of_nonzero IsFractional.div_of_nonzeroₓ'. -/
 theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     IsFractional R₁⁰ I → IsFractional R₁⁰ J → J ≠ 0 → IsFractional R₁⁰ (I / J)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩, h =>
@@ -1685,9 +1097,6 @@ theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     rw [← hy', mul_comm b, ← Algebra.smul_def, mul_smul]
 #align is_fractional.div_of_nonzero IsFractional.div_of_nonzero
 
-/- warning: fractional_ideal.fractional_div_of_nonzero -> FractionalIdeal.fractional_div_of_nonzero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.fractional_div_of_nonzero FractionalIdeal.fractional_div_of_nonzeroₓ'. -/
 theorem fractional_div_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     IsFractional R₁⁰ (I / J : Submodule R₁ K) :=
   I.IsFractional.div_of_nonzero J.IsFractional fun H =>
@@ -1699,45 +1108,27 @@ noncomputable instance : Div (FractionalIdeal R₁⁰ K) :=
 
 variable {I J : FractionalIdeal R₁⁰ K} [J ≠ 0]
 
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 @[simp]
 theorem div_zero {I : FractionalIdeal R₁⁰ K} : I / 0 = 0 :=
   dif_pos rfl
 #align fractional_ideal.div_zero FractionalIdeal.div_zero
 
-/- warning: fractional_ideal.div_nonzero -> FractionalIdeal.div_nonzero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_nonzero FractionalIdeal.div_nonzeroₓ'. -/
 theorem div_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     I / J = ⟨I / J, fractional_div_of_nonzero h⟩ :=
   dif_neg h
 #align fractional_ideal.div_nonzero FractionalIdeal.div_nonzero
 
-/- warning: fractional_ideal.coe_div -> FractionalIdeal.coe_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_div FractionalIdeal.coe_divₓ'. -/
 @[simp]
 theorem coe_div {I J : FractionalIdeal R₁⁰ K} (hJ : J ≠ 0) :
     (↑(I / J) : Submodule R₁ K) = ↑I / (↑J : Submodule R₁ K) :=
   congr_arg _ (dif_neg hJ)
 #align fractional_ideal.coe_div FractionalIdeal.coe_div
 
-/- warning: fractional_ideal.mem_div_iff_of_nonzero -> FractionalIdeal.mem_div_iff_of_nonzero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzeroₓ'. -/
 theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {x} :
     x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I := by rw [div_nonzero h];
   exact Submodule.mem_div_iff_forall_mul_mem
 #align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzero
 
-/- warning: fractional_ideal.mul_one_div_le_one -> FractionalIdeal.mul_one_div_le_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_oneₓ'. -/
 theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :=
   by
   by_cases hI : I = 0
@@ -1747,9 +1138,6 @@ theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :
     apply Submodule.mul_one_div_le_one
 #align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_one
 
-/- warning: fractional_ideal.le_self_mul_one_div -> FractionalIdeal.le_self_mul_one_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_divₓ'. -/
 theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
     I ≤ I * (1 / I) := by
   by_cases hI_nz : I = 0
@@ -1759,18 +1147,12 @@ theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : Fra
     exact Submodule.le_self_mul_one_div hI
 #align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_div
 
-/- warning: fractional_ideal.le_div_iff_of_nonzero -> FractionalIdeal.le_div_iff_of_nonzero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzeroₓ'. -/
 theorem le_div_iff_of_nonzero {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ ∀ x ∈ I, ∀ y ∈ J', x * y ∈ J :=
   ⟨fun h x hx => (mem_div_iff_of_nonzero hJ').mp (h hx), fun h x hx =>
     (mem_div_iff_of_nonzero hJ').mpr (h x hx)⟩
 #align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzero
 
-/- warning: fractional_ideal.le_div_iff_mul_le -> FractionalIdeal.le_div_iff_mul_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_div_iff_mul_le FractionalIdeal.le_div_iff_mul_leₓ'. -/
 theorem le_div_iff_mul_le {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ I * J' ≤ J := by
   rw [div_nonzero hJ']
@@ -1778,12 +1160,6 @@ theorem le_div_iff_mul_le {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0)
   rw [← coe_mul, coe_le_coe]
 #align fractional_ideal.le_div_iff_mul_le FractionalIdeal.le_div_iff_mul_le
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_one FractionalIdeal.div_oneₓ'. -/
 @[simp]
 theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I :=
   by
@@ -1798,9 +1174,6 @@ theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I :=
     exact (Algebra.smul_def _ _).symm
 #align fractional_ideal.div_one FractionalIdeal.div_one
 
-/- warning: fractional_ideal.eq_one_div_of_mul_eq_one_right -> FractionalIdeal.eq_one_div_of_mul_eq_one_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_rightₓ'. -/
 theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : J = 1 / I :=
   by
   have hI : I ≠ 0 := ne_zero_of_mul_eq_one I J h
@@ -1822,18 +1195,12 @@ theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I
   exact mul_mem_mul hx hy
 #align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_right
 
-/- warning: fractional_ideal.mul_div_self_cancel_iff -> FractionalIdeal.mul_div_self_cancel_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iffₓ'. -/
 theorem mul_div_self_cancel_iff {I : FractionalIdeal R₁⁰ K} : I * (1 / I) = 1 ↔ ∃ J, I * J = 1 :=
   ⟨fun h => ⟨1 / I, h⟩, fun ⟨J, hJ⟩ => by rwa [← eq_one_div_of_mul_eq_one_right I J hJ]⟩
 #align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iff
 
 variable {K' : Type _} [Field K'] [Algebra R₁ K'] [IsFractionRing R₁ K']
 
-/- warning: fractional_ideal.map_div -> FractionalIdeal.map_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_div FractionalIdeal.map_divₓ'. -/
 @[simp]
 theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     (I / J).map (h : K →ₐ[R₁] K') = I.map h / J.map h :=
@@ -1844,9 +1211,6 @@ theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     simp [div_nonzero H, div_nonzero (map_ne_zero _ H), Submodule.map_div]
 #align fractional_ideal.map_div FractionalIdeal.map_div
 
-/- warning: fractional_ideal.map_one_div -> FractionalIdeal.map_one_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_one_div FractionalIdeal.map_one_divₓ'. -/
 @[simp]
 theorem map_one_div (I : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     (1 / I).map (h : K →ₐ[R₁] K') = 1 / I.map h := by rw [map_div, map_one]
@@ -1860,12 +1224,6 @@ variable {R₁ K L : Type _} [CommRing R₁] [Field K] [Field L]
 
 variable [Algebra R₁ K] [IsFractionRing R₁ K] [Algebra K L] [IsFractionRing K L]
 
-/- warning: fractional_ideal.eq_zero_or_one -> FractionalIdeal.eq_zero_or_one is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_oneₓ'. -/
 theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
   by
   rw [or_iff_not_imp_left]
@@ -1883,12 +1241,6 @@ theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
     exact Submodule.smul_mem I _ y_mem
 #align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_one
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_zero_or_one_of_is_field FractionalIdeal.eq_zero_or_one_of_isFieldₓ'. -/
 theorem eq_zero_or_one_of_isField (hF : IsField R₁) (I : FractionalIdeal R₁⁰ K) : I = 0 ∨ I = 1 :=
   letI : Field R₁ := hF.to_field
   eq_zero_or_one I
@@ -1923,12 +1275,6 @@ def spanFinset {ι : Type _} (s : Finset ι) (f : ι → K) : FractionalIdeal R
 
 variable {R₁}
 
-/- warning: fractional_ideal.span_finset_eq_zero -> FractionalIdeal.spanFinset_eq_zero is a dubious translation:
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 @[simp]
 theorem spanFinset_eq_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f = 0 ↔ ∀ j ∈ s, f j = 0 := by
@@ -1936,12 +1282,6 @@ theorem spanFinset_eq_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     Set.mem_image, Finset.mem_coe, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
 #align fractional_ideal.span_finset_eq_zero FractionalIdeal.spanFinset_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_finset_ne_zero FractionalIdeal.spanFinset_ne_zeroₓ'. -/
 theorem spanFinset_ne_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f ≠ 0 ↔ ∃ j ∈ s, f j ≠ 0 := by simp
 #align fractional_ideal.span_finset_ne_zero FractionalIdeal.spanFinset_ne_zero
@@ -1950,12 +1290,6 @@ open Submodule.IsPrincipal
 
 include loc
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_span_singleton FractionalIdeal.isFractional_span_singletonₓ'. -/
 theorem isFractional_span_singleton (x : P) : IsFractional S (span R {x} : Submodule R P) :=
   let ⟨a, ha⟩ := exists_integer_multiple S x
   isFractional_span_iff.mpr ⟨a, a.2, fun x' hx' => (Set.mem_singleton_iff.mp hx').symm ▸ ha⟩
@@ -1993,21 +1327,12 @@ theorem mem_spanSingleton_self (x : P) : x ∈ spanSingleton S x :=
 
 variable {S}
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_le_iff_mem FractionalIdeal.spanSingleton_le_iff_memₓ'. -/
 @[simp]
 theorem spanSingleton_le_iff_mem {x : P} {I : FractionalIdeal S P} :
     spanSingleton S x ≤ I ↔ x ∈ I := by
   rw [← coe_le_coe, coe_span_singleton, Submodule.span_singleton_le_iff_mem x ↑I, mem_coe]
 #align fractional_ideal.span_singleton_le_iff_mem FractionalIdeal.spanSingleton_le_iff_mem
 
-/- warning: fractional_ideal.span_singleton_eq_span_singleton -> FractionalIdeal.spanSingleton_eq_spanSingleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_eq_span_singleton FractionalIdeal.spanSingleton_eq_spanSingletonₓ'. -/
 theorem spanSingleton_eq_spanSingleton [NoZeroSMulDivisors R P] {x y : P} :
     spanSingleton S x = spanSingleton S y ↔ ∃ z : Rˣ, z • x = y :=
   by
@@ -2015,68 +1340,32 @@ theorem spanSingleton_eq_spanSingleton [NoZeroSMulDivisors R P] {x y : P} :
   exact Subtype.mk_eq_mk
 #align fractional_ideal.span_singleton_eq_span_singleton FractionalIdeal.spanSingleton_eq_spanSingleton
 
-/- warning: fractional_ideal.eq_span_singleton_of_principal -> FractionalIdeal.eq_spanSingleton_of_principal is a dubious translation:
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 theorem eq_spanSingleton_of_principal (I : FractionalIdeal S P) [IsPrincipal (I : Submodule R P)] :
     I = spanSingleton S (generator (I : Submodule R P)) := by rw [span_singleton];
   exact coe_to_submodule_injective (span_singleton_generator ↑I).symm
 #align fractional_ideal.eq_span_singleton_of_principal FractionalIdeal.eq_spanSingleton_of_principal
 
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 theorem isPrincipal_iff (I : FractionalIdeal S P) :
     IsPrincipal (I : Submodule R P) ↔ ∃ x, I = spanSingleton S x :=
   ⟨fun h => ⟨@generator _ _ _ _ _ (↑I) h, @eq_spanSingleton_of_principal _ _ _ _ _ _ _ I h⟩,
     fun ⟨x, hx⟩ => { principal := ⟨x, trans (congr_arg _ hx) (coe_spanSingleton _ x)⟩ }⟩
 #align fractional_ideal.is_principal_iff FractionalIdeal.isPrincipal_iff
 
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 @[simp]
 theorem spanSingleton_zero : spanSingleton S (0 : P) = 0 := by ext;
   simp [Submodule.mem_span_singleton, eq_comm]
 #align fractional_ideal.span_singleton_zero FractionalIdeal.spanSingleton_zero
 
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 theorem spanSingleton_eq_zero_iff {y : P} : spanSingleton S y = 0 ↔ y = 0 :=
   ⟨fun h =>
     span_eq_bot.mp (by simpa using congr_arg Subtype.val h : span R {y} = ⊥) y (mem_singleton y),
     fun h => by simp [h]⟩
 #align fractional_ideal.span_singleton_eq_zero_iff FractionalIdeal.spanSingleton_eq_zero_iff
 
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 theorem spanSingleton_ne_zero_iff {y : P} : spanSingleton S y ≠ 0 ↔ y ≠ 0 :=
   not_congr spanSingleton_eq_zero_iff
 #align fractional_ideal.span_singleton_ne_zero_iff FractionalIdeal.spanSingleton_ne_zero_iff
 
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 @[simp]
 theorem spanSingleton_one : spanSingleton S (1 : P) = 1 :=
   by
@@ -2086,12 +1375,6 @@ theorem spanSingleton_one : spanSingleton S (1 : P) = 1 :=
   rw [Algebra.smul_def, mul_one]
 #align fractional_ideal.span_singleton_one FractionalIdeal.spanSingleton_one
 
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 @[simp]
 theorem spanSingleton_mul_spanSingleton (x y : P) :
     spanSingleton S x * spanSingleton S y = spanSingleton S (x * y) :=
@@ -2100,12 +1383,6 @@ theorem spanSingleton_mul_spanSingleton (x y : P) :
   simp only [coe_mul, coe_span_singleton, span_mul_span, singleton_mul_singleton]
 #align fractional_ideal.span_singleton_mul_span_singleton FractionalIdeal.spanSingleton_mul_spanSingleton
 
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 @[simp]
 theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingleton S (x ^ n) :=
   by
@@ -2114,12 +1391,6 @@ theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingle
   · rw [pow_succ, hn, span_singleton_mul_span_singleton, pow_succ]
 #align fractional_ideal.span_singleton_pow FractionalIdeal.spanSingleton_pow
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coeIdeal_span_singletonₓ'. -/
 @[simp]
 theorem coeIdeal_span_singleton (x : R) :
     (↑(Ideal.span {x} : Ideal R) : FractionalIdeal S P) = spanSingleton S (algebraMap R P x) :=
@@ -2136,9 +1407,6 @@ theorem coeIdeal_span_singleton (x : R) :
     rw [RingHom.map_mul, Algebra.smul_def]
 #align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coeIdeal_span_singleton
 
-/- warning: fractional_ideal.canonical_equiv_span_singleton -> FractionalIdeal.canonicalEquiv_spanSingleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingletonₓ'. -/
 @[simp]
 theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocalization S P']
     (x : P) :
@@ -2163,12 +1431,6 @@ theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocali
     simp [IsLocalization.map_smul]
 #align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingleton
 
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 theorem mem_singleton_mul {x y : P} {I : FractionalIdeal S P} :
     y ∈ spanSingleton S x * I ↔ ∃ y' ∈ I, y = x * y' :=
   by
@@ -2189,9 +1451,6 @@ omit loc
 
 variable (K)
 
-/- warning: fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal -> FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdealₓ'. -/
 theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈ R₁⁰) :
     spanSingleton R₁⁰ (IsLocalization.mk' K x ⟨y, hy⟩) * I = (J : FractionalIdeal R₁⁰ K) ↔
       Ideal.span {x} * I = Ideal.span {y} * J :=
@@ -2214,9 +1473,6 @@ theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈
 
 variable {K}
 
-/- warning: fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal -> FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdealₓ'. -/
 theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
     spanSingleton R₁⁰ z * (I : FractionalIdeal R₁⁰ K) = J ↔
       Ideal.span {((IsLocalization.sec R₁⁰ z).1 : R₁)} * I =
@@ -2228,22 +1484,10 @@ theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
 
 variable [IsDomain R₁]
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.one_div_span_singleton FractionalIdeal.one_div_spanSingletonₓ'. -/
 theorem one_div_spanSingleton (x : K) : 1 / spanSingleton R₁⁰ x = spanSingleton R₁⁰ x⁻¹ :=
   if h : x = 0 then by simp [h] else (eq_one_div_of_mul_eq_one_right _ _ (by simp [h])).symm
 #align fractional_ideal.one_div_span_singleton FractionalIdeal.one_div_spanSingleton
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingletonₓ'. -/
 @[simp]
 theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
     J / spanSingleton R₁⁰ d = spanSingleton R₁⁰ d⁻¹ * J :=
@@ -2264,9 +1508,6 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
     exact le_refl J
 #align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingleton
 
-/- warning: fractional_ideal.exists_eq_span_singleton_mul -> FractionalIdeal.exists_eq_spanSingleton_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mulₓ'. -/
 theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
     ∃ (a : R₁)(aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI :=
   by
@@ -2307,24 +1548,12 @@ instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Alg
 
 include loc
 
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_span_singleton_mul_iff FractionalIdeal.le_spanSingleton_mul_iffₓ'. -/
 theorem le_spanSingleton_mul_iff {x : P} {I J : FractionalIdeal S P} :
     I ≤ spanSingleton S x * J ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI :=
   show (∀ {zI} (hzI : zI ∈ I), zI ∈ spanSingleton _ x * J) ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI by
     simp only [mem_singleton_mul, eq_comm]
 #align fractional_ideal.le_span_singleton_mul_iff FractionalIdeal.le_spanSingleton_mul_iff
 
-/- warning: fractional_ideal.span_singleton_mul_le_iff -> FractionalIdeal.spanSingleton_mul_le_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_mul_le_iff FractionalIdeal.spanSingleton_mul_le_iffₓ'. -/
 theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
     spanSingleton _ x * I ≤ J ↔ ∀ z ∈ I, x * z ∈ J :=
   by
@@ -2337,9 +1566,6 @@ theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
     exact Submodule.smul_mem J.1 _ (h zI hzI)
 #align fractional_ideal.span_singleton_mul_le_iff FractionalIdeal.spanSingleton_mul_le_iff
 
-/- warning: fractional_ideal.eq_span_singleton_mul -> FractionalIdeal.eq_spanSingleton_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_span_singleton_mul FractionalIdeal.eq_spanSingleton_mulₓ'. -/
 theorem eq_spanSingleton_mul {x : P} {I J : FractionalIdeal S P} :
     I = spanSingleton _ x * J ↔ (∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI) ∧ ∀ z ∈ J, x * z ∈ I := by
   simp only [le_antisymm_iff, le_span_singleton_mul_iff, span_singleton_mul_le_iff]
@@ -2353,25 +1579,16 @@ variable {K : Type _} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
 attribute [local instance] Classical.propDecidable
 
-/- warning: fractional_ideal.is_noetherian_zero -> FractionalIdeal.isNoetherian_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zeroₓ'. -/
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
   isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by rw [coe_zero] at hI;
     rw [le_bot_iff.mp hI]; exact fg_bot
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 
-/- warning: fractional_ideal.is_noetherian_iff -> FractionalIdeal.isNoetherian_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iffₓ'. -/
 theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
     IsNoetherian R₁ I ↔ ∀ J ≤ I, (J : Submodule R₁ K).FG :=
   isNoetherian_submodule.trans ⟨fun h J hJ => h _ hJ, fun h J hJ => h ⟨J, isFractional_of_le hJ⟩ hJ⟩
 #align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iff
 
-/- warning: fractional_ideal.is_noetherian_coe_ideal -> FractionalIdeal.isNoetherian_coeIdeal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_coe_ideal FractionalIdeal.isNoetherian_coeIdealₓ'. -/
 theorem isNoetherian_coeIdeal [IsNoetherianRing R₁] (I : Ideal R₁) :
     IsNoetherian R₁ (I : FractionalIdeal R₁⁰ K) :=
   by
@@ -2385,9 +1602,6 @@ include frac
 
 variable [IsDomain R₁]
 
-/- warning: fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul -> FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulₓ'. -/
 theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdeal R₁⁰ K}
     (hI : IsNoetherian R₁ I) :
     IsNoetherian R₁ (spanSingleton R₁⁰ (algebraMap R₁ K x)⁻¹ * I : FractionalIdeal R₁⁰ K) :=
@@ -2408,9 +1622,6 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
     mul_one]
 #align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul
 
-/- warning: fractional_ideal.is_noetherian -> FractionalIdeal.isNoetherian is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian FractionalIdeal.isNoetherianₓ'. -/
 /-- Every fractional ideal of a noetherian integral domain is noetherian. -/
 theorem isNoetherian [IsNoetherianRing R₁] (I : FractionalIdeal R₁⁰ K) : IsNoetherian R₁ I :=
   by
@@ -2427,9 +1638,6 @@ omit frac
 
 variable {R P} (S) (x : P) (hx : IsIntegral R x)
 
-/- warning: fractional_ideal.is_fractional_adjoin_integral -> FractionalIdeal.isFractional_adjoin_integral is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integralₓ'. -/
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Algebra.adjoin R ({x} : Set P)).toSubmodule :=

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

@@ -175,11 +175,7 @@ theorem ext {I J : FractionalIdeal S P} : (∀ x, x ∈ I ↔ x ∈ J) → I = J
 /-- Copy of a `fractional_ideal` with a new underlying set equal to the old one.
 Useful to fix definitional equalities. -/
 protected def copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : FractionalIdeal S P :=
-  ⟨Submodule.copy p s hs, by
-    convert p.is_fractional
-    ext
-    simp only [hs]
-    rfl⟩
+  ⟨Submodule.copy p s hs, by convert p.is_fractional; ext; simp only [hs]; rfl⟩
 #align fractional_ideal.copy FractionalIdeal.copy
 -/
 
@@ -826,10 +822,8 @@ theorem mul_def (I J : FractionalIdeal S P) : I * J = ⟨I * J, I.IsFractional.m
 <too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_mul FractionalIdeal.coe_mulₓ'. -/
 @[simp, norm_cast]
-theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I * J :=
-  by
-  simp only [mul_def]
-  rfl
+theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I * J := by
+  simp only [mul_def]; rfl
 #align fractional_ideal.coe_mul FractionalIdeal.coe_mul
 
 /- warning: fractional_ideal.coe_ideal_mul -> FractionalIdeal.coeIdeal_mul is a dubious translation:
@@ -878,9 +872,7 @@ but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {i : P} {j : P}, (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) i I) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) j J) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) i j) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_mem_mul FractionalIdeal.mul_mem_mulₓ'. -/
 theorem mul_mem_mul {I J : FractionalIdeal S P} {i j : P} (hi : i ∈ I) (hj : j ∈ J) :
-    i * j ∈ I * J := by
-  simp only [mul_def]
-  exact Submodule.mul_mem_mul hi hj
+    i * j ∈ I * J := by simp only [mul_def]; exact Submodule.mul_mem_mul hi hj
 #align fractional_ideal.mul_mem_mul FractionalIdeal.mul_mem_mul
 
 /- warning: fractional_ideal.mul_le -> FractionalIdeal.mul_le is a dubious translation:
@@ -889,10 +881,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {K : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J) K) (forall (i : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) i I) -> (forall (j : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) j J) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) i j) K)))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_le FractionalIdeal.mul_leₓ'. -/
-theorem mul_le {I J K : FractionalIdeal S P} : I * J ≤ K ↔ ∀ i ∈ I, ∀ j ∈ J, i * j ∈ K :=
-  by
-  simp only [mul_def]
-  exact Submodule.mul_le
+theorem mul_le {I J K : FractionalIdeal S P} : I * J ≤ K ↔ ∀ i ∈ I, ∀ j ∈ J, i * j ∈ K := by
+  simp only [mul_def]; exact Submodule.mul_le
 #align fractional_ideal.mul_le FractionalIdeal.mul_le
 
 instance : Pow (FractionalIdeal S P) ℕ :=
@@ -1322,16 +1312,9 @@ theorem isFractional_span_iff {s : Set P} :
     IsFractional S (span R s) ↔ ∃ a ∈ S, ∀ b : P, b ∈ s → IsInteger R (a • b) :=
   ⟨fun ⟨a, a_mem, h⟩ => ⟨a, a_mem, fun b hb => h b (subset_span hb)⟩, fun ⟨a, a_mem, h⟩ =>
     ⟨a, a_mem, fun b hb =>
-      span_induction hb h
-        (by
-          rw [smul_zero]
-          exact is_integer_zero)
-        (fun x y hx hy => by
-          rw [smul_add]
-          exact is_integer_add hx hy)
-        fun s x hx => by
-        rw [smul_comm]
-        exact is_integer_smul hx⟩⟩
+      span_induction hb h (by rw [smul_zero]; exact is_integer_zero)
+        (fun x y hx hy => by rw [smul_add]; exact is_integer_add hx hy) fun s x hx => by
+        rw [smul_comm]; exact is_integer_smul hx⟩⟩
 #align fractional_ideal.is_fractional_span_iff FractionalIdeal.isFractional_span_iff
 
 include loc
@@ -1402,9 +1385,7 @@ but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))], (Function.Injective.{succ u2, succ u1} R P (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))))) (algebraMap.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3))) -> (forall (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))), (IsUnit.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)) -> (Ideal.FG.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) I))
 Case conversion may be inaccurate. Consider using '#align ideal.fg_of_is_unit Ideal.fg_of_isUnitₓ'. -/
 theorem Ideal.fg_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
-    (h : IsUnit (I : FractionalIdeal S P)) : I.FG :=
-  by
-  rw [← coe_ideal_fg S inj I]
+    (h : IsUnit (I : FractionalIdeal S P)) : I.FG := by rw [← coe_ideal_fg S inj I];
   exact fg_of_is_unit I h
 #align ideal.fg_of_is_unit Ideal.fg_of_isUnit
 
@@ -1493,9 +1474,7 @@ theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type _) [CommRing P''] [Algeb
 <too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coeIdealₓ'. -/
 @[simp]
-theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I :=
-  by
-  ext
+theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I := by ext;
   simp [IsLocalization.map_eq]
 #align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coeIdeal
 
@@ -1661,9 +1640,7 @@ variable [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
 instance : Nontrivial (FractionalIdeal R₁⁰ K) :=
   ⟨⟨0, 1, fun h =>
-      have this : (1 : K) ∈ (0 : FractionalIdeal R₁⁰ K) :=
-        by
-        rw [← (algebraMap R₁ K).map_one]
+      have this : (1 : K) ∈ (0 : FractionalIdeal R₁⁰ K) := by rw [← (algebraMap R₁ K).map_one];
         simpa only [h] using coe_mem_one R₁⁰ 1
       one_ne_zero ((mem_zero_iff _).mp this)⟩⟩
 
@@ -1674,10 +1651,7 @@ but is expected to have type
   forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] (I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6), (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) I J) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.ne_zero_of_mul_eq_one FractionalIdeal.ne_zero_of_mul_eq_oneₓ'. -/
 theorem ne_zero_of_mul_eq_one (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : I ≠ 0 := fun hI =>
-  zero_ne_one' (FractionalIdeal R₁⁰ K)
-    (by
-      convert h
-      simp [hI])
+  zero_ne_one' (FractionalIdeal R₁⁰ K) (by convert h; simp [hI])
 #align fractional_ideal.ne_zero_of_mul_eq_one FractionalIdeal.ne_zero_of_mul_eq_one
 
 variable [IsDomain R₁]
@@ -1757,8 +1731,7 @@ theorem coe_div {I J : FractionalIdeal R₁⁰ K} (hJ : J ≠ 0) :
 <too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzeroₓ'. -/
 theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {x} :
-    x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I := by
-  rw [div_nonzero h]
+    x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I := by rw [div_nonzero h];
   exact Submodule.mem_div_iff_forall_mul_mem
 #align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzero
 
@@ -1780,8 +1753,7 @@ Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_se
 theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
     I ≤ I * (1 / I) := by
   by_cases hI_nz : I = 0
-  · rw [hI_nz, div_zero, MulZeroClass.mul_zero]
-    exact zero_le 0
+  · rw [hI_nz, div_zero, MulZeroClass.mul_zero]; exact zero_le 0
   · rw [← coe_le_coe, coe_mul, coe_div hI_nz, coe_one]
     rw [← coe_le_coe, coe_one] at hI
     exact Submodule.le_self_mul_one_div hI
@@ -1942,16 +1914,10 @@ def spanFinset {ι : Type _} (s : Finset ι) (f : ι → K) : FractionalIdeal R
     by
     obtain ⟨a', ha'⟩ := IsLocalization.exist_integer_multiples R₁⁰ s f
     refine' ⟨a', a'.2, fun x hx => Submodule.span_induction hx _ _ _ _⟩
-    · rintro _ ⟨i, hi, rfl⟩
-      exact ha' i hi
-    · rw [smul_zero]
-      exact IsLocalization.isInteger_zero
-    · intro x y hx hy
-      rw [smul_add]
-      exact IsLocalization.isInteger_add hx hy
-    · intro c x hx
-      rw [smul_comm]
-      exact IsLocalization.isInteger_smul hx⟩
+    · rintro _ ⟨i, hi, rfl⟩; exact ha' i hi
+    · rw [smul_zero]; exact IsLocalization.isInteger_zero
+    · intro x y hx hy; rw [smul_add]; exact IsLocalization.isInteger_add hx hy
+    · intro c x hx; rw [smul_comm]; exact IsLocalization.isInteger_smul hx⟩
 #align fractional_ideal.span_finset FractionalIdeal.spanFinset
 -/
 
@@ -2007,19 +1973,15 @@ irreducible_def spanSingleton (x : P) : FractionalIdeal S P :=
 #print FractionalIdeal.coe_spanSingleton /-
 -- local attribute [semireducible] span_singleton
 @[simp]
-theorem coe_spanSingleton (x : P) : (spanSingleton S x : Submodule R P) = span R {x} :=
-  by
-  rw [span_singleton]
-  rfl
+theorem coe_spanSingleton (x : P) : (spanSingleton S x : Submodule R P) = span R {x} := by
+  rw [span_singleton]; rfl
 #align fractional_ideal.coe_span_singleton FractionalIdeal.coe_spanSingleton
 -/
 
 #print FractionalIdeal.mem_spanSingleton /-
 @[simp]
-theorem mem_spanSingleton {x y : P} : x ∈ spanSingleton S y ↔ ∃ z : R, z • y = x :=
-  by
-  rw [span_singleton]
-  exact Submodule.mem_span_singleton
+theorem mem_spanSingleton {x y : P} : x ∈ spanSingleton S y ↔ ∃ z : R, z • y = x := by
+  rw [span_singleton]; exact Submodule.mem_span_singleton
 #align fractional_ideal.mem_span_singleton FractionalIdeal.mem_spanSingleton
 -/
 
@@ -2060,9 +2022,7 @@ but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) [_inst_8 : Submodule.IsPrincipal.{u2, u1} R P (CommRing.toRing.{u2} R _inst_1) (Ring.toAddCommGroup.{u1} P (CommRing.toRing.{u1} P _inst_2)) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)], Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc (Submodule.IsPrincipal.generator.{u2, u1} R P (Ring.toAddCommGroup.{u1} P (CommRing.toRing.{u1} P _inst_2)) (CommRing.toRing.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) _inst_8))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_span_singleton_of_principal FractionalIdeal.eq_spanSingleton_of_principalₓ'. -/
 theorem eq_spanSingleton_of_principal (I : FractionalIdeal S P) [IsPrincipal (I : Submodule R P)] :
-    I = spanSingleton S (generator (I : Submodule R P)) :=
-  by
-  rw [span_singleton]
+    I = spanSingleton S (generator (I : Submodule R P)) := by rw [span_singleton];
   exact coe_to_submodule_injective (span_singleton_generator ↑I).symm
 #align fractional_ideal.eq_span_singleton_of_principal FractionalIdeal.eq_spanSingleton_of_principal
 
@@ -2085,9 +2045,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3], Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc (OfNat.ofNat.{u2} P 0 (Zero.toOfNat0.{u2} P (CommMonoidWithZero.toZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_zero FractionalIdeal.spanSingleton_zeroₓ'. -/
 @[simp]
-theorem spanSingleton_zero : spanSingleton S (0 : P) = 0 :=
-  by
-  ext
+theorem spanSingleton_zero : spanSingleton S (0 : P) = 0 := by ext;
   simp [Submodule.mem_span_singleton, eq_comm]
 #align fractional_ideal.span_singleton_zero FractionalIdeal.spanSingleton_zero
 
@@ -2339,10 +2297,8 @@ instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Alg
   by
   obtain ⟨a, aI, -, ha⟩ := exists_eq_span_singleton_mul I
   use (algebraMap R K a)⁻¹ * algebraMap R K (generator aI)
-  suffices I = span_singleton R⁰ ((algebraMap R K a)⁻¹ * algebraMap R K (generator aI))
-    by
-    rw [span_singleton] at this
-    exact congr_arg Subtype.val this
+  suffices I = span_singleton R⁰ ((algebraMap R K a)⁻¹ * algebraMap R K (generator aI)) by
+    rw [span_singleton] at this; exact congr_arg Subtype.val this
   conv_lhs => rw [ha, ← span_singleton_generator aI]
   rw [Ideal.submodule_span_eq, coe_ideal_span_singleton (generator aI),
     span_singleton_mul_span_singleton]
@@ -2401,11 +2357,8 @@ attribute [local instance] Classical.propDecidable
 <too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zeroₓ'. -/
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
-  isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) =>
-    by
-    rw [coe_zero] at hI
-    rw [le_bot_iff.mp hI]
-    exact fg_bot
+  isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by rw [coe_zero] at hI;
+    rw [le_bot_iff.mp hI]; exact fg_bot
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 
 /- warning: fractional_ideal.is_noetherian_iff -> FractionalIdeal.isNoetherian_iff is a dubious translation:

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

@@ -218,10 +218,7 @@ theorem val_eq_coe (I : FractionalIdeal S P) : I.val = I :=
 #align fractional_ideal.val_eq_coe FractionalIdeal.val_eq_coe
 
 /- warning: fractional_ideal.coe_mk -> FractionalIdeal.coe_mk is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_mk FractionalIdeal.coe_mkₓ'. -/
 @[simp, norm_cast]
 theorem coe_mk (I : Submodule R P) (hI : IsFractional S I) :
@@ -312,10 +309,7 @@ theorem coe_coeIdeal (I : Ideal R) :
 variable (S)
 
 /- warning: fractional_ideal.mem_coe_ideal -> FractionalIdeal.mem_coeIdeal is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_coe_ideal FractionalIdeal.mem_coeIdealₓ'. -/
 @[simp]
 theorem mem_coeIdeal {x : P} {I : Ideal R} :
@@ -403,10 +397,7 @@ variable (P)
 include loc
 
 /- warning: fractional_ideal.exists_mem_to_map_eq -> FractionalIdeal.exists_mem_algebraMap_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_mem_to_map_eq FractionalIdeal.exists_mem_algebraMap_eqₓ'. -/
 @[simp]
 theorem exists_mem_algebraMap_eq {x : R} {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
@@ -570,10 +561,7 @@ and ports the lattice structure on submodules to fractional ideals.
 
 
 /- warning: fractional_ideal.coe_le_coe -> FractionalIdeal.coe_le_coe is a dubious translation:
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(FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J)) (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I J)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J)) (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) I J)
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_le_coe FractionalIdeal.coe_le_coeₓ'. -/
 @[simp]
 theorem coe_le_coe {I J : FractionalIdeal S P} :
@@ -676,10 +664,7 @@ instance : Inf (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊓ J, I.IsFractional.inf_right J⟩⟩
 
 /- warning: fractional_ideal.coe_inf -> FractionalIdeal.coe_inf is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_inf FractionalIdeal.coe_infₓ'. -/
 @[simp, norm_cast]
 theorem coe_inf (I J : FractionalIdeal S P) : ↑(I ⊓ J) = (I ⊓ J : Submodule R P) :=
@@ -690,10 +675,7 @@ instance : Sup (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊔ J, I.IsFractional.sup J.IsFractional⟩⟩
 
 /- warning: fractional_ideal.coe_sup -> FractionalIdeal.coe_sup is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_sup FractionalIdeal.coe_supₓ'. -/
 @[norm_cast]
 theorem coe_sup (I J : FractionalIdeal S P) : ↑(I ⊔ J) = (I ⊔ J : Submodule R P) :=
@@ -728,10 +710,7 @@ theorem sup_eq_add (I J : FractionalIdeal S P) : I ⊔ J = I + J :=
 #align fractional_ideal.sup_eq_add FractionalIdeal.sup_eq_add
 
 /- warning: fractional_ideal.coe_add -> FractionalIdeal.coe_add is a dubious translation:
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(Semiring.toNonAssocSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3))))))) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_add FractionalIdeal.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add (I J : FractionalIdeal S P) : (↑(I + J) : Submodule R P) = I + J :=
@@ -750,10 +729,7 @@ theorem coeIdeal_sup (I J : Ideal R) : ↑(I ⊔ J) = (I + J : FractionalIdeal S
 #align fractional_ideal.coe_ideal_sup FractionalIdeal.coeIdeal_sup
 
 /- warning: is_fractional.nsmul -> IsFractional.nsmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_fractional.nsmul IsFractional.nsmulₓ'. -/
 theorem IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
@@ -769,10 +745,7 @@ theorem IsFractional.nsmul {I : Submodule R P} :
 instance : SMul ℕ (FractionalIdeal S P) where smul n I := ⟨n • I, I.IsFractional.nsmul n⟩
 
 /- warning: fractional_ideal.coe_nsmul -> FractionalIdeal.coe_nsmul is a dubious translation:
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-but is expected to have type
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(CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))))) n (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_nsmul FractionalIdeal.coe_nsmulₓ'. -/
 @[norm_cast]
 theorem coe_nsmul (n : ℕ) (I : FractionalIdeal S P) : (↑(n • I) : Submodule R P) = n • I :=
@@ -843,20 +816,14 @@ theorem mul_eq_mul (I J : FractionalIdeal S P) : mul I J = I * J :=
 #align fractional_ideal.mul_eq_mul FractionalIdeal.mul_eq_mul
 
 /- warning: fractional_ideal.mul_def -> FractionalIdeal.mul_def is a dubious translation:
-lean 3 declaration is
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(Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) => IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.mul.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J)) (IsFractional.mul.{u1, u2} R _inst_1 S P _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J) (FractionalIdeal.isFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.isFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 J)))
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_def FractionalIdeal.mul_defₓ'. -/
 theorem mul_def (I J : FractionalIdeal S P) : I * J = ⟨I * J, I.IsFractional.mul J.IsFractional⟩ :=
   by simp only [← mul_eq_mul, mul]
 #align fractional_ideal.mul_def FractionalIdeal.mul_def
 
 /- warning: fractional_ideal.coe_mul -> FractionalIdeal.coe_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_mul FractionalIdeal.coe_mulₓ'. -/
 @[simp, norm_cast]
 theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I * J :=
@@ -932,10 +899,7 @@ instance : Pow (FractionalIdeal S P) ℕ :=
   ⟨fun I n => ⟨I ^ n, I.IsFractional.pow n⟩⟩
 
 /- warning: fractional_ideal.coe_pow -> FractionalIdeal.coe_pow is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) n)
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_pow FractionalIdeal.coe_powₓ'. -/
 @[simp, norm_cast]
 theorem coe_pow (I : FractionalIdeal S P) (n : ℕ) : ↑(I ^ n) = (I ^ n : Submodule R P) :=
@@ -960,10 +924,7 @@ instance : NatCast (FractionalIdeal S P) :=
   ⟨Nat.unaryCast⟩
 
 /- warning: fractional_ideal.coe_nat_cast -> FractionalIdeal.coe_nat_cast is a dubious translation:
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(CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))))))) n)
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_castₓ'. -/
 theorem coe_nat_cast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
   show ↑n.unaryCast = ↑n by induction n <;> simp [*, Nat.unaryCast]
@@ -1166,10 +1127,7 @@ def map (g : P →ₐ[R] P') : FractionalIdeal S P → FractionalIdeal S P' := f
 -/
 
 /- warning: fractional_ideal.coe_map -> FractionalIdeal.coe_map is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] (g : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u3} (Submodule.{u1, u3} R P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5)) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (Submodule.{u1, u3} R P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5)) (HasLiftT.mk.{succ u3, succ u3} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (Submodule.{u1, u3} R P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5)) (CoeTCₓ.coe.{succ u3, succ u3} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (Submodule.{u1, u3} R P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5)) (coeBase.{succ u3, succ u3} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (Submodule.{u1, u3} R P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5)) (FractionalIdeal.Submodule.hasCoe.{u1, u3} R _inst_1 S P' _inst_4 _inst_5)))) (FractionalIdeal.map.{u1, u2, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R P P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) P P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R P P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgHom.toLinearMap.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5 g) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I))
-but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] (g : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (FractionalIdeal.coeToSubmodule.{u3, u1} R _inst_1 S P' _inst_4 _inst_5 (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I)) (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R P P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) P P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R P P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (AlgHom.toLinearMap.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 g) (FractionalIdeal.coeToSubmodule.{u3, u2} R _inst_1 S P _inst_2 _inst_3 I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_map FractionalIdeal.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map (g : P →ₐ[R] P') (I : FractionalIdeal S P) :
@@ -1178,10 +1136,7 @@ theorem coe_map (g : P →ₐ[R] P') (I : FractionalIdeal S P) :
 #align fractional_ideal.coe_map FractionalIdeal.coe_map
 
 /- warning: fractional_ideal.mem_map -> FractionalIdeal.mem_map is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_map FractionalIdeal.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {I : FractionalIdeal S P} {g : P →ₐ[R] P'} {y : P'} :
@@ -1199,10 +1154,7 @@ theorem map_id : I.map (AlgHom.id _ _) = I :=
 -/
 
 /- warning: fractional_ideal.map_comp -> FractionalIdeal.map_comp is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_comp FractionalIdeal.map_compₓ'. -/
 @[simp]
 theorem map_comp (g' : P' →ₐ[R] P'') : I.map (g'.comp g) = (I.map g).map g' :=
@@ -1274,10 +1226,7 @@ theorem map_mul : (I * J).map g = I.map g * J.map g :=
 #align fractional_ideal.map_mul FractionalIdeal.map_mul
 
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 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_map_symm FractionalIdeal.map_map_symmₓ'. -/
 @[simp]
 theorem map_map_symm (g : P ≃ₐ[R] P') : (I.map (g : P →ₐ[R] P')).map (g.symm : P' →ₐ[R] P) = I := by
@@ -1285,10 +1234,7 @@ theorem map_map_symm (g : P ≃ₐ[R] P') : (I.map (g : P →ₐ[R] P')).map (g.
 #align fractional_ideal.map_map_symm FractionalIdeal.map_map_symm
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_symm_map FractionalIdeal.map_symm_mapₓ'. -/
 @[simp]
 theorem map_symm_map (I : FractionalIdeal S P') (g : P ≃ₐ[R] P') :
@@ -1297,10 +1243,7 @@ theorem map_symm_map (I : FractionalIdeal S P') (g : P ≃ₐ[R] P') :
 #align fractional_ideal.map_symm_map FractionalIdeal.map_symm_map
 
 /- warning: fractional_ideal.map_mem_map -> FractionalIdeal.map_mem_map is a dubious translation:
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R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f)) -> (forall {x : P} {I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') x) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f x) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f I)) (Membership.mem.{u2, u2} P (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)) x I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_mem_map FractionalIdeal.map_mem_mapₓ'. -/
 theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I : FractionalIdeal S P} :
     f x ∈ map f I ↔ x ∈ I :=
@@ -1308,10 +1251,7 @@ theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I :
 #align fractional_ideal.map_mem_map FractionalIdeal.map_mem_map
 
 /- warning: fractional_ideal.map_injective -> FractionalIdeal.map_injective is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_injective FractionalIdeal.map_injectiveₓ'. -/
 theorem map_injective (f : P →ₐ[R] P') (h : Function.Injective f) :
     Function.Injective (map f : FractionalIdeal S P → FractionalIdeal S P') := fun I J hIJ =>
@@ -1336,10 +1276,7 @@ def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S
 #align fractional_ideal.map_equiv FractionalIdeal.mapEquiv
 
 /- warning: fractional_ideal.coe_fun_map_equiv -> FractionalIdeal.coeFun_mapEquiv is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coeFun_mapEquivₓ'. -/
 @[simp]
 theorem coeFun_mapEquiv (g : P ≃ₐ[R] P') :
@@ -1348,10 +1285,7 @@ theorem coeFun_mapEquiv (g : P ≃ₐ[R] P') :
 #align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coeFun_mapEquiv
 
 /- warning: fractional_ideal.map_equiv_apply -> FractionalIdeal.mapEquiv_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_equiv_apply FractionalIdeal.mapEquiv_applyₓ'. -/
 @[simp]
 theorem mapEquiv_apply (g : P ≃ₐ[R] P') (I : FractionalIdeal S P) : mapEquiv g I = map (↑g) I :=
@@ -1382,10 +1316,7 @@ theorem mapEquiv_refl : mapEquiv AlgEquiv.refl = RingEquiv.refl (FractionalIdeal
 #align fractional_ideal.map_equiv_refl FractionalIdeal.mapEquiv_refl
 
 /- warning: fractional_ideal.is_fractional_span_iff -> FractionalIdeal.isFractional_span_iff is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_span_iff FractionalIdeal.isFractional_span_iffₓ'. -/
 theorem isFractional_span_iff {s : Set P} :
     IsFractional S (span R s) ↔ ∃ a ∈ S, ∀ b : P, b ∈ s → IsInteger R (a • b) :=
@@ -1422,10 +1353,7 @@ theorem isFractional_of_fg {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
 omit loc
 
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 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_span_mul_finite_of_mem_mul FractionalIdeal.mem_span_mul_finite_of_mem_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx : x ∈ I * J) :
     ∃ T T' : Finset P, (T : Set P) ⊆ I ∧ (T' : Set P) ⊆ J ∧ x ∈ span R (T * T' : Set P) :=
@@ -1501,10 +1429,7 @@ noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* Fractio
 #align fractional_ideal.canonical_equiv FractionalIdeal.canonicalEquiv
 
 /- warning: fractional_ideal.mem_canonical_equiv_apply -> FractionalIdeal.mem_canonicalEquiv_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_canonical_equiv_apply FractionalIdeal.mem_canonicalEquiv_applyₓ'. -/
 @[simp]
 theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
@@ -1535,20 +1460,14 @@ theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P'
 #align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symm
 
 /- warning: fractional_ideal.canonical_equiv_flip -> FractionalIdeal.canonicalEquiv_flip is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flipₓ'. -/
 theorem canonicalEquiv_flip (I) : canonicalEquiv S P P' (canonicalEquiv S P' P I) = I := by
   rw [← canonical_equiv_symm, RingEquiv.symm_apply_apply]
 #align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flip
 
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(CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} P'' (CommRing.toCommSemiring.{u4} P'' _inst_8))] [_inst_10 : IsLocalization.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) S P'' (CommRing.toCommSemiring.{u4} P'' _inst_8) _inst_9] (I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) => FractionalIdeal.{u3, u4} R _inst_1 S P'' _inst_8 _inst_9) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingEquiv.{u2, u1} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instMulFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instAddFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u3, u1} R _inst_1 S P' 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 Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquivₓ'. -/
 @[simp]
 theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
@@ -1562,10 +1481,7 @@ theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P
 #align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquiv
 
 /- warning: fractional_ideal.canonical_equiv_trans_canonical_equiv -> FractionalIdeal.canonicalEquiv_trans_canonicalEquiv is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_trans_canonical_equiv FractionalIdeal.canonicalEquiv_trans_canonicalEquivₓ'. -/
 theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] :
@@ -1574,10 +1490,7 @@ theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type _) [CommRing P''] [Algeb
 #align fractional_ideal.canonical_equiv_trans_canonical_equiv FractionalIdeal.canonicalEquiv_trans_canonicalEquiv
 
 /- warning: fractional_ideal.canonical_equiv_coe_ideal -> FractionalIdeal.canonicalEquiv_coeIdeal is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coeIdealₓ'. -/
 @[simp]
 theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I :=
@@ -1621,10 +1534,7 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
 /- warning: fractional_ideal.exists_ne_zero_mem_is_integer -> FractionalIdeal.exists_ne_zero_mem_isInteger is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_ne_zero_mem_is_integer FractionalIdeal.exists_ne_zero_mem_isIntegerₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 /-- Nonzero fractional ideals contain a nonzero integer. -/
@@ -1657,10 +1567,7 @@ theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 :=
 #align fractional_ideal.map_ne_zero FractionalIdeal.map_ne_zero
 
 /- warning: fractional_ideal.map_eq_zero_iff -> FractionalIdeal.map_eq_zero_iff is a dubious translation:
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-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {K : Type.{u1}} {K' : Type.{u2}} [_inst_4 : Field.{u1} K] [_inst_5 : Field.{u2} K'] [_inst_6 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))] [_inst_7 : IsFractionRing.{u3, u1} R _inst_1 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6] [_inst_8 : Algebra.{u3, u2} R K' (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u2} K' (Semifield.toDivisionSemiring.{u2} K' (Field.toSemifield.{u2} K' _inst_5)))] [_inst_9 : IsFractionRing.{u3, u2} R _inst_1 K' (EuclideanDomain.toCommRing.{u2} K' (Field.toEuclideanDomain.{u2} K' _inst_5)) _inst_8] {I : FractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6} (h : AlgHom.{u3, u1, u2} R K K' (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) (DivisionSemiring.toSemiring.{u2} K' (Semifield.toDivisionSemiring.{u2} K' (Field.toSemifield.{u2} K' _inst_5))) _inst_6 _inst_8) [_inst_10 : Nontrivial.{u3} R], Iff (Eq.{succ u2} (FractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u2} K' (Field.toEuclideanDomain.{u2} K' _inst_5)) _inst_8) (FractionalIdeal.map.{u3, u1, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6 K' (EuclideanDomain.toCommRing.{u2} K' (Field.toEuclideanDomain.{u2} K' _inst_5)) _inst_8 h I) (OfNat.ofNat.{u2} (FractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u2} K' (Field.toEuclideanDomain.{u2} K' _inst_5)) _inst_8) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u2} K' (Field.toEuclideanDomain.{u2} K' _inst_5)) _inst_8) (FractionalIdeal.instZeroFractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u2} K' (Field.toEuclideanDomain.{u2} K' _inst_5)) _inst_8)))) (Eq.{succ u1} (FractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) I (OfNat.ofNat.{u1} (FractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_eq_zero_iff FractionalIdeal.map_eq_zero_iffₓ'. -/
 @[simp]
 theorem map_eq_zero_iff [Nontrivial R] : I.map h = 0 ↔ I = 0 :=
@@ -1778,10 +1685,7 @@ variable [IsDomain R₁]
 include frac
 
 /- warning: is_fractional.div_of_nonzero -> IsFractional.div_of_nonzero is a dubious translation:
-lean 3 declaration is
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R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) J (OfNat.ofNat.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) 0 (OfNat.mk.{u2} 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_inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.idemSemiring.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)))))))))) -> (IsFractional.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (instHDiv.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.hasDiv.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) _inst_6)) I J))
-but is expected to have type
-  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)} {J : Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)}, (IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) -> (IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J) -> (Ne.{succ u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) J (OfNat.ofNat.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) 0 (Zero.toOfNat0.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (CommMonoidWithZero.toZero.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (CommSemiring.toCommMonoidWithZero.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (IdemCommSemiring.toCommSemiring.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6))))))) -> (IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (instHDiv.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6)) I J))
+<too large>
 Case conversion may be inaccurate. Consider using '#align is_fractional.div_of_nonzero IsFractional.div_of_nonzeroₓ'. -/
 theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     IsFractional R₁⁰ I → IsFractional R₁⁰ J → J ≠ 0 → IsFractional R₁⁰ (I / J)
@@ -1808,10 +1712,7 @@ theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
 #align is_fractional.div_of_nonzero IsFractional.div_of_nonzero
 
 /- warning: fractional_ideal.fractional_div_of_nonzero -> FractionalIdeal.fractional_div_of_nonzero is a dubious translation:
-lean 3 declaration is
-  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K 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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.fractional_div_of_nonzero FractionalIdeal.fractional_div_of_nonzeroₓ'. -/
 theorem fractional_div_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     IsFractional R₁⁰ (I / J : Submodule R₁ K) :=
@@ -1836,10 +1737,7 @@ theorem div_zero {I : FractionalIdeal R₁⁰ K} : I / 0 = 0 :=
 #align fractional_ideal.div_zero FractionalIdeal.div_zero
 
 /- warning: fractional_ideal.div_nonzero -> FractionalIdeal.div_nonzero is a dubious translation:
-lean 3 declaration is
-  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} (h : Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))), Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J) (Subtype.mk.{succ u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (fun (I : Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) => IsFractional.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 I) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (instHDiv.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.hasDiv.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) J)) (FractionalIdeal.fractional_div_of_nonzero.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7 I J h))
-but is expected to have type
-  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} (h : Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) J (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ 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(Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J) (Subtype.mk.{succ u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (fun (I : Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) => IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (instHDiv.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6)) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J)) (FractionalIdeal.fractional_div_of_nonzero.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7 I J h))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_nonzero FractionalIdeal.div_nonzeroₓ'. -/
 theorem div_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     I / J = ⟨I / J, fractional_div_of_nonzero h⟩ :=
@@ -1847,10 +1745,7 @@ theorem div_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
 #align fractional_ideal.div_nonzero FractionalIdeal.div_nonzero
 
 /- warning: fractional_ideal.coe_div -> FractionalIdeal.coe_div is a dubious translation:
-lean 3 declaration is
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HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) J)))
-but is expected to have type
-  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, (Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) J (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ 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(CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 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(EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (instHDiv.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6)) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_div FractionalIdeal.coe_divₓ'. -/
 @[simp]
 theorem coe_div {I J : FractionalIdeal R₁⁰ K} (hJ : J ≠ 0) :
@@ -1859,10 +1754,7 @@ theorem coe_div {I J : FractionalIdeal R₁⁰ K} (hJ : J ≠ 0) :
 #align fractional_ideal.coe_div FractionalIdeal.coe_div
 
 /- warning: fractional_ideal.mem_div_iff_of_nonzero -> FractionalIdeal.mem_div_iff_of_nonzero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzeroₓ'. -/
 theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {x} :
     x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I := by
@@ -1871,10 +1763,7 @@ theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {
 #align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzero
 
 /- warning: fractional_ideal.mul_one_div_le_one -> FractionalIdeal.mul_one_div_le_one is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_oneₓ'. -/
 theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :=
   by
@@ -1886,10 +1775,7 @@ theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :
 #align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_one
 
 /- warning: fractional_ideal.le_self_mul_one_div -> FractionalIdeal.le_self_mul_one_div is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_divₓ'. -/
 theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
     I ≤ I * (1 / I) := by
@@ -1902,10 +1788,7 @@ theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : Fra
 #align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_div
 
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R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.lattice.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))) I (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) J J')) (forall (x : K), (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) x I) -> (forall (y : K), (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) y J') -> (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) x y) J))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzeroₓ'. -/
 theorem le_div_iff_of_nonzero {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ ∀ x ∈ I, ∀ y ∈ J', x * y ∈ J :=
@@ -1914,10 +1797,7 @@ theorem le_div_iff_of_nonzero {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠
 #align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzero
 
 /- warning: fractional_ideal.le_div_iff_mul_le -> FractionalIdeal.le_div_iff_mul_le is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_div_iff_mul_le FractionalIdeal.le_div_iff_mul_leₓ'. -/
 theorem le_div_iff_mul_le {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ I * J' ≤ J := by
@@ -1947,10 +1827,7 @@ theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I :=
 #align fractional_ideal.div_one FractionalIdeal.div_one
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_rightₓ'. -/
 theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : J = 1 / I :=
   by
@@ -1974,10 +1851,7 @@ theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I
 #align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_right
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iffₓ'. -/
 theorem mul_div_self_cancel_iff {I : FractionalIdeal R₁⁰ K} : I * (1 / I) = 1 ↔ ∃ J, I * J = 1 :=
   ⟨fun h => ⟨1 / I, h⟩, fun ⟨J, hJ⟩ => by rwa [← eq_one_div_of_mul_eq_one_right I J hJ]⟩
@@ -1986,10 +1860,7 @@ theorem mul_div_self_cancel_iff {I : FractionalIdeal R₁⁰ K} : I * (1 / I) =
 variable {K' : Type _} [Field K'] [Algebra R₁ K'] [IsFractionRing R₁ K']
 
 /- warning: fractional_ideal.map_div -> FractionalIdeal.map_div is a dubious translation:
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K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u3, u1, u2, u3} (AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (Ring.toSemiring.{u3} K' (CommRing.toRing.{u3} K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.algEquivClass.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10))))) h) J))
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-  forall {R₁ : Type.{u3}} [_inst_4 : CommRing.{u3} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u3, u2} R₁ K (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))] [frac : IsFractionRing.{u3, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4))] {K' : Type.{u1}} [_inst_9 : Field.{u1} K'] [_inst_10 : Algebra.{u3, u1} R₁ K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9)))] [_inst_11 : IsFractionRing.{u3, u1} R₁ _inst_4 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10] (I : FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (J : FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (h : AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10), Eq.{succ u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' 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(CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10 (AlgHomClass.toAlgHom.{u3, u2, u1, max u2 u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (CommSemiring.toSemiring.{u1} K' (CommRing.toCommSemiring.{u1} K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} 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_inst_10)) h) J))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_div FractionalIdeal.map_divₓ'. -/
 @[simp]
 theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
@@ -2002,10 +1873,7 @@ theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
 #align fractional_ideal.map_div FractionalIdeal.map_div
 
 /- warning: fractional_ideal.map_one_div -> FractionalIdeal.map_one_div is a dubious translation:
-lean 3 declaration is
-  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {K' : Type.{u3}} [_inst_9 : Field.{u3} K'] [_inst_10 : Algebra.{u1, u3} R₁ K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9)))] [_inst_11 : IsFractionRing.{u1, u3} R₁ _inst_4 K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)) _inst_10] (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ 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(Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))) I)) (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (instHDiv.{u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ 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(Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10)) h) I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_one_div FractionalIdeal.map_one_divₓ'. -/
 @[simp]
 theorem map_one_div (I : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
@@ -2176,10 +2044,7 @@ theorem spanSingleton_le_iff_mem {x : P} {I : FractionalIdeal S P} :
 #align fractional_ideal.span_singleton_le_iff_mem FractionalIdeal.spanSingleton_le_iff_mem
 
 /- warning: fractional_ideal.span_singleton_eq_span_singleton -> FractionalIdeal.spanSingleton_eq_spanSingleton is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_eq_span_singleton FractionalIdeal.spanSingleton_eq_spanSingletonₓ'. -/
 theorem spanSingleton_eq_spanSingleton [NoZeroSMulDivisors R P] {x y : P} :
     spanSingleton S x = spanSingleton S y ↔ ∃ z : Rˣ, z • x = y :=
@@ -2314,10 +2179,7 @@ theorem coeIdeal_span_singleton (x : R) :
 #align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coeIdeal_span_singleton
 
 /- warning: fractional_ideal.canonical_equiv_span_singleton -> FractionalIdeal.canonicalEquiv_spanSingleton is a dubious translation:
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(CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y) S) => this) hy)) x))
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-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {P' : Type.{u3}} [_inst_8 : CommRing.{u3} P'] [_inst_9 : Algebra.{u2, u3} R P' (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_8))] [_inst_10 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S P' (CommRing.toCommSemiring.{u3} P' _inst_8) _inst_9] (x : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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(RingHom.instRingHomClassRingHom.{u2, u2} R R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) y) S) => this) hy])) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingletonₓ'. -/
 @[simp]
 theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocalization S P']
@@ -2370,10 +2232,7 @@ omit loc
 variable (K)
 
 /- warning: fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal -> FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal is a dubious translation:
-lean 3 declaration is
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(CommRing.toRing.{u1} R₁ _inst_4))) (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (instHMul.{u1} (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (Ideal.hasMul.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Ideal.span.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (Singleton.singleton.{u1, u1} R₁ (Set.{u1} R₁) (Set.hasSingleton.{u1} R₁) y)) J))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdealₓ'. -/
 theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈ R₁⁰) :
     spanSingleton R₁⁰ (IsLocalization.mk' K x ⟨y, hy⟩) * I = (J : FractionalIdeal R₁⁰ K) ↔
@@ -2398,10 +2257,7 @@ theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈
 variable {K}
 
 /- warning: fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal -> FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdealₓ'. -/
 theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
     spanSingleton R₁⁰ z * (I : FractionalIdeal R₁⁰ K) = J ↔
@@ -2451,10 +2307,7 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
 #align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingleton
 
 /- warning: fractional_ideal.exists_eq_span_singleton_mul -> FractionalIdeal.exists_eq_spanSingleton_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mulₓ'. -/
 theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
     ∃ (a : R₁)(aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI :=
@@ -2529,10 +2382,7 @@ theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
 #align fractional_ideal.span_singleton_mul_le_iff FractionalIdeal.spanSingleton_mul_le_iff
 
 /- warning: fractional_ideal.eq_span_singleton_mul -> FractionalIdeal.eq_spanSingleton_mul is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_span_singleton_mul FractionalIdeal.eq_spanSingleton_mulₓ'. -/
 theorem eq_spanSingleton_mul {x : P} {I J : FractionalIdeal S P} :
     I = spanSingleton _ x * J ↔ (∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI) ∧ ∀ z ∈ J, x * z ∈ I := by
@@ -2548,10 +2398,7 @@ variable {K : Type _} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 attribute [local instance] Classical.propDecidable
 
 /- warning: fractional_ideal.is_noetherian_zero -> FractionalIdeal.isNoetherian_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zeroₓ'. -/
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
   isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) =>
@@ -2562,10 +2409,7 @@ theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 
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(CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6))) x (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)) 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(Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.lattice.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))) J I) -> (Submodule.FG.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iffₓ'. -/
 theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
     IsNoetherian R₁ I ↔ ∀ J ≤ I, (J : Submodule R₁ K).FG :=
@@ -2573,10 +2417,7 @@ theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
 #align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iff
 
 /- warning: fractional_ideal.is_noetherian_coe_ideal -> FractionalIdeal.isNoetherian_coeIdeal is a dubious translation:
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-  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [_inst_7 : IsNoetherianRing.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] (I : Ideal.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))), IsNoetherian.{u2, u1} R₁ (Subtype.{succ u1} K (fun (x : K) => Membership.mem.{u1, u1} K (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) K (Submodule.setLike.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6))) x (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (FractionalIdeal.coeIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (FractionalIdeal.coeIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (FractionalIdeal.coeIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_coe_ideal FractionalIdeal.isNoetherian_coeIdealₓ'. -/
 theorem isNoetherian_coeIdeal [IsNoetherianRing R₁] (I : Ideal R₁) :
     IsNoetherian R₁ (I : FractionalIdeal R₁⁰ K) :=
@@ -2592,10 +2433,7 @@ include frac
 variable [IsDomain R₁]
 
 /- warning: fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul -> FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul is a dubious translation:
-lean 3 declaration is
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R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)))) _inst_6)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Submodule.setLike.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)))) _inst_6))) x_1 (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 frac (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ (fun (a : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonUnitalNonAssocSemiring.toMul.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))))) (algebraMap.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6) x))) I)))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 frac (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonUnitalNonAssocSemiring.toMul.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))))) (algebraMap.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6) x))) I))) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 frac (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulₓ'. -/
 theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdeal R₁⁰ K}
     (hI : IsNoetherian R₁ I) :
@@ -2618,10 +2456,7 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
 #align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul
 
 /- warning: fractional_ideal.is_noetherian -> FractionalIdeal.isNoetherian is a dubious translation:
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-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian FractionalIdeal.isNoetherianₓ'. -/
 /-- Every fractional ideal of a noetherian integral domain is noetherian. -/
 theorem isNoetherian [IsNoetherianRing R₁] (I : FractionalIdeal R₁⁰ K) : IsNoetherian R₁ I :=
@@ -2640,10 +2475,7 @@ omit frac
 variable {R P} (S) (x : P) (hx : IsIntegral R x)
 
 /- warning: fractional_ideal.is_fractional_adjoin_integral -> FractionalIdeal.isFractional_adjoin_integral is a dubious translation:
-lean 3 declaration is
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R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.adjoin.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3 (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.hasSingleton.{u2} P) x))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] (x : P), (IsIntegral.{u2, u1} R P _inst_1 (CommRing.toRing.{u1} P _inst_2) _inst_3 x) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Submodule.{u2, u1} R P 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(CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) P (Subalgebra.instSetLikeSubalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Algebra.adjoin.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3 (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) x))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integralₓ'. -/
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Filippo A. E. Nuccio
 
 ! This file was ported from Lean 3 source module ring_theory.fractional_ideal
-! leanprover-community/mathlib commit ed90a7d327c3a5caf65a6faf7e8a0d63c4605df7
+! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,6 +19,9 @@ import Mathbin.Tactic.FieldSimp
 /-!
 # Fractional ideals
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines fractional ideals of an integral domain and proves basic facts about them.
 
 ## Main definitions

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

@@ -1178,7 +1178,7 @@ theorem coe_map (g : P →ₐ[R] P') (I : FractionalIdeal S P) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {g : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5} {y : P'}, Iff (Membership.Mem.{u3, u3} P' (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.setLike.{u1, u3} R _inst_1 S P' _inst_4 _inst_5)) y (FractionalIdeal.map.{u1, u2, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I)) (Exists.{succ u2} P (fun (x : P) => And (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x I) (Eq.{succ u3} P' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) => P -> P') ([anonymous].{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) g x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] {I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3} {g : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5} {y : P'}, Iff (Membership.mem.{u1, u1} P' (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5)) y (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I)) (Exists.{succ u2} P (fun (x : P) => And (Membership.mem.{u2, u2} P (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)) x I) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) g x) y)))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] {I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3} {g : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5} {y : P'}, Iff (Membership.mem.{u1, u1} P' (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5)) y (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I)) (Exists.{succ u2} P (fun (x : P) => And (Membership.mem.{u2, u2} P (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)) x I) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) g x) y)))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_map FractionalIdeal.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {I : FractionalIdeal S P} {g : P →ₐ[R] P'} {y : P'} :
@@ -1297,7 +1297,7 @@ theorem map_symm_map (I : FractionalIdeal S P') (g : P ≃ₐ[R] P') :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] {f : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u3} P P' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) => P -> P') ([anonymous].{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) f)) -> (forall {x : P} {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Membership.Mem.{u3, u3} P' (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (SetLike.hasMem.{u3, u3} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.setLike.{u1, u3} R _inst_1 S P' _inst_4 _inst_5)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) => P -> P') ([anonymous].{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) f x) (FractionalIdeal.map.{u1, u2, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f I)) (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x I))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] {f : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u1} P P' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f)) -> (forall {x : P} {I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') x) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f x) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f I)) (Membership.mem.{u2, u2} P (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)) x I))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] {f : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u1} P P' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f)) -> (forall {x : P} {I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') x) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f x) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f I)) (Membership.mem.{u2, u2} P (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)) x I))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_mem_map FractionalIdeal.map_mem_mapₓ'. -/
 theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I : FractionalIdeal S P} :
     f x ∈ map f I ↔ x ∈ I :=
@@ -1308,7 +1308,7 @@ theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] (f : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u3} P P' (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) (fun (_x : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) => P -> P') ([anonymous].{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) f)) -> (Function.Injective.{succ u2, succ u3} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.map.{u1, u2, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f))
 but is expected to have type
-  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] (f : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u1} P P' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f)) -> (Function.Injective.{succ u2, succ u1} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f))
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] (f : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5), (Function.Injective.{succ u2, succ u1} P P' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f)) -> (Function.Injective.{succ u2, succ u1} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f))
 Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_injective FractionalIdeal.map_injectiveₓ'. -/
 theorem map_injective (f : P →ₐ[R] P') (h : Function.Injective f) :
     Function.Injective (map f : FractionalIdeal S P → FractionalIdeal S P') := fun I J hIJ =>

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

@@ -86,13 +86,16 @@ variable [Algebra R P]
 
 variable (S)
 
+#print IsFractional /-
 /-- A submodule `I` is a fractional ideal if `a I ⊆ R` for some `a ≠ 0`. -/
 def IsFractional (I : Submodule R P) :=
   ∃ a ∈ S, ∀ b ∈ I, IsInteger R (a • b)
 #align is_fractional IsFractional
+-/
 
 variable (S P)
 
+#print FractionalIdeal /-
 /-- The fractional ideals of a domain `R` are ideals of `R` divided by some `a ∈ R`.
 
   More precisely, let `P` be a localization of `R` at some submonoid `S`,
@@ -102,6 +105,7 @@ variable (S P)
 def FractionalIdeal :=
   { I : Submodule R P // IsFractional S I }
 #align fractional_ideal FractionalIdeal
+-/
 
 end Defs
 
@@ -125,6 +129,12 @@ not to be confused with `is_localization.coe_submodule : ideal R → submodule R
 instance : Coe (FractionalIdeal S P) (Submodule R P) :=
   ⟨fun I => I.val⟩
 
+/- warning: fractional_ideal.is_fractional -> FractionalIdeal.isFractional is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional FractionalIdeal.isFractionalₓ'. -/
 protected theorem isFractional (I : FractionalIdeal S P) : IsFractional S (I : Submodule R P) :=
   I.Prop
 #align fractional_ideal.is_fractional FractionalIdeal.isFractional
@@ -136,16 +146,29 @@ instance : SetLike (FractionalIdeal S P) P
   coe I := ↑(I : Submodule R P)
   coe_injective' := SetLike.coe_injective.comp Subtype.coe_injective
 
+/- warning: fractional_ideal.mem_coe -> FractionalIdeal.mem_coe is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_coe FractionalIdeal.mem_coeₓ'. -/
 @[simp]
 theorem mem_coe {I : FractionalIdeal S P} {x : P} : x ∈ (I : Submodule R P) ↔ x ∈ I :=
   Iff.rfl
 #align fractional_ideal.mem_coe FractionalIdeal.mem_coe
 
+/- warning: fractional_ideal.ext -> FractionalIdeal.ext is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, (forall (x : P), Iff (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x I) (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x J)) -> (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I J)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.ext FractionalIdeal.extₓ'. -/
 @[ext]
 theorem ext {I J : FractionalIdeal S P} : (∀ x, x ∈ I ↔ x ∈ J) → I = J :=
   SetLike.ext
 #align fractional_ideal.ext FractionalIdeal.ext
 
+#print FractionalIdeal.copy /-
 /-- Copy of a `fractional_ideal` with a new underlying set equal to the old one.
 Useful to fix definitional equalities. -/
 protected def copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : FractionalIdeal S P :=
@@ -155,23 +178,48 @@ protected def copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : Fract
     simp only [hs]
     rfl⟩
 #align fractional_ideal.copy FractionalIdeal.copy
+-/
 
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (p : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (s : Set.{u1} P) (hs : Eq.{succ u1} (Set.{u1} P) s (SetLike.coe.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) p)), Eq.{succ u1} (Set.{u1} P) (SetLike.coe.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.copy.{u2, u1} R _inst_1 S P _inst_2 _inst_3 p s hs)) s
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_copy FractionalIdeal.coe_copyₓ'. -/
 @[simp]
 theorem coe_copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : ↑(p.copy s hs) = s :=
   rfl
 #align fractional_ideal.coe_copy FractionalIdeal.coe_copy
 
+/- warning: fractional_ideal.coe_eq -> FractionalIdeal.coe_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (p : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (s : Set.{u2} P) (hs : Eq.{succ u2} (Set.{u2} P) s ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Set.{u2} P) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Set.{u2} P) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Set.{u2} P) (SetLike.Set.hasCoeT.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) p)), Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.copy.{u1, u2} R _inst_1 S P _inst_2 _inst_3 p s hs) p
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (p : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (s : Set.{u1} P) (hs : Eq.{succ u1} (Set.{u1} P) s (SetLike.coe.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) p)), Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.copy.{u2, u1} R _inst_1 S P _inst_2 _inst_3 p s hs) p
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_eq FractionalIdeal.coe_eqₓ'. -/
 theorem coe_eq (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : p.copy s hs = p :=
   SetLike.coe_injective hs
 #align fractional_ideal.coe_eq FractionalIdeal.coe_eq
 
 end SetLike
 
+/- warning: fractional_ideal.val_eq_coe -> FractionalIdeal.val_eq_coe is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Subtype.val.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) => IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Subtype.val.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (fun (I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) => IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.val_eq_coe FractionalIdeal.val_eq_coeₓ'. -/
 @[simp]
 theorem val_eq_coe (I : FractionalIdeal S P) : I.val = I :=
   rfl
 #align fractional_ideal.val_eq_coe FractionalIdeal.val_eq_coe
 
+/- warning: fractional_ideal.coe_mk -> FractionalIdeal.coe_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (hI : IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subtype.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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(NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) => IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) => IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (Subtype.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) => IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeSubtype.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) => IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I))))) (Subtype.mk.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (fun (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) => IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) I hI)) I
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (hI : IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (Subtype.mk.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (fun (I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) => IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) I hI)) I
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_mk FractionalIdeal.coe_mkₓ'. -/
 @[simp, norm_cast]
 theorem coe_mk (I : Submodule R P) (hI : IsFractional S I) :
     (Subtype.mk I hI : Submodule R P) = I :=
@@ -187,15 +235,28 @@ instance (I : FractionalIdeal S P) : AddCommGroup I :=
 instance (I : FractionalIdeal S P) : Module R I :=
   Submodule.module ↑I
 
-theorem coe_to_submodule_injective :
-    Function.Injective (coe : FractionalIdeal S P → Submodule R P) :=
+#print FractionalIdeal.coeToSubmodule_injective /-
+theorem coeToSubmodule_injective : Function.Injective (coe : FractionalIdeal S P → Submodule R P) :=
   Subtype.coe_injective
-#align fractional_ideal.coe_to_submodule_injective FractionalIdeal.coe_to_submodule_injective
-
-theorem coe_to_submodule_inj {I J : FractionalIdeal S P} : (I : Submodule R P) = J ↔ I = J :=
-  coe_to_submodule_injective.eq_iff
-#align fractional_ideal.coe_to_submodule_inj FractionalIdeal.coe_to_submodule_inj
+#align fractional_ideal.coe_to_submodule_injective FractionalIdeal.coeToSubmodule_injective
+-/
 
+/- warning: fractional_ideal.coe_to_submodule_inj -> FractionalIdeal.coeToSubmodule_inj is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J)) (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I J)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J)) (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I J)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_to_submodule_inj FractionalIdeal.coeToSubmodule_injₓ'. -/
+theorem coeToSubmodule_inj {I J : FractionalIdeal S P} : (I : Submodule R P) = J ↔ I = J :=
+  coeToSubmodule_injective.eq_iff
+#align fractional_ideal.coe_to_submodule_inj FractionalIdeal.coeToSubmodule_inj
+
+/- warning: fractional_ideal.is_fractional_of_le_one -> FractionalIdeal.isFractional_of_le_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)), (LE.le.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) P (Submodule.setLike.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.one.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)), (LE.le.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) I (OfNat.ofNat.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) 1 (One.toOfNat1.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.one.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_of_le_one FractionalIdeal.isFractional_of_le_oneₓ'. -/
 theorem isFractional_of_le_one (I : Submodule R P) (h : I ≤ 1) : IsFractional S I :=
   by
   use 1, S.one_mem
@@ -205,6 +266,12 @@ theorem isFractional_of_le_one (I : Submodule R P) (h : I ≤ 1) : IsFractional
   exact Set.mem_range_self b'
 #align fractional_ideal.is_fractional_of_le_one FractionalIdeal.isFractional_of_le_one
 
+/- warning: fractional_ideal.is_fractional_of_le -> FractionalIdeal.isFractional_of_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} 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(NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J)) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) I (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J)) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_of_le FractionalIdeal.isFractional_of_leₓ'. -/
 theorem isFractional_of_le {I : Submodule R P} {J : FractionalIdeal S P} (hIJ : I ≤ J) :
     IsFractional S I := by
   obtain ⟨a, a_mem, ha⟩ := J.is_fractional
@@ -227,39 +294,75 @@ instance : CoeTC (Ideal R) (FractionalIdeal S P) :=
     ⟨coeSubmodule P I,
       isFractional_of_le_one _ <| by simpa using coe_submodule_mono P (le_top : I ≤ ⊤)⟩⟩
 
+/- warning: fractional_ideal.coe_coe_ideal -> FractionalIdeal.coe_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I)) (IsLocalization.coeSubmodule.{u1, u2} R _inst_1 P _inst_2 _inst_3 I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)) (IsLocalization.coeSubmodule.{u2, u1} R _inst_1 P _inst_2 _inst_3 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_coe_ideal FractionalIdeal.coe_coeIdealₓ'. -/
 @[simp, norm_cast]
-theorem coe_coe_ideal (I : Ideal R) :
+theorem coe_coeIdeal (I : Ideal R) :
     ((I : FractionalIdeal S P) : Submodule R P) = coeSubmodule P I :=
   rfl
-#align fractional_ideal.coe_coe_ideal FractionalIdeal.coe_coe_ideal
+#align fractional_ideal.coe_coe_ideal FractionalIdeal.coe_coeIdeal
 
 variable (S)
 
+/- warning: fractional_ideal.mem_coe_ideal -> FractionalIdeal.mem_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {x : P} {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I)) (Exists.{succ u1} R (fun (x' : R) => And (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x' I) (Eq.{succ u2} P (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (fun (_x : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) => R -> P) (RingHom.hasCoeToFun.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (algebraMap.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) x') x)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {x : P} {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, Iff (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) x (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)) (Exists.{succ u2} R (fun (x' : R) => And (Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) x' I) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x') (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))))) (algebraMap.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) x') x)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_coe_ideal FractionalIdeal.mem_coeIdealₓ'. -/
 @[simp]
-theorem mem_coe_ideal {x : P} {I : Ideal R} :
+theorem mem_coeIdeal {x : P} {I : Ideal R} :
     x ∈ (I : FractionalIdeal S P) ↔ ∃ x', x' ∈ I ∧ algebraMap R P x' = x :=
   mem_coeSubmodule _ _
-#align fractional_ideal.mem_coe_ideal FractionalIdeal.mem_coe_ideal
-
-theorem mem_coe_ideal_of_mem {x : R} {I : Ideal R} (hx : x ∈ I) :
+#align fractional_ideal.mem_coe_ideal FractionalIdeal.mem_coeIdeal
+
+/- warning: fractional_ideal.mem_coe_ideal_of_mem -> FractionalIdeal.mem_coeIdeal_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {x : R} {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x I) -> (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (fun (_x : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) => R -> P) (RingHom.hasCoeToFun.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (algebraMap.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) x) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {x : R} {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) x I) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))) R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R P (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))))) (algebraMap.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) x) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_coe_ideal_of_mem FractionalIdeal.mem_coeIdeal_of_memₓ'. -/
+theorem mem_coeIdeal_of_mem {x : R} {I : Ideal R} (hx : x ∈ I) :
     algebraMap R P x ∈ (I : FractionalIdeal S P) :=
-  (mem_coe_ideal S).mpr ⟨x, hx, rfl⟩
-#align fractional_ideal.mem_coe_ideal_of_mem FractionalIdeal.mem_coe_ideal_of_mem
-
-theorem coe_ideal_le_coe_ideal' [IsLocalization S P] (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
+  (mem_coeIdeal S).mpr ⟨x, hx, rfl⟩
+#align fractional_ideal.mem_coe_ideal_of_mem FractionalIdeal.mem_coeIdeal_of_mem
+
+/- warning: fractional_ideal.coe_ideal_le_coe_ideal' -> FractionalIdeal.coeIdeal_le_coeIdeal' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [_inst_4 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) J)) (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) I J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [_inst_4 : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) S (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {J : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J)) (LE.le.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Preorder.toLE.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (PartialOrder.toPreorder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.completeLattice.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_le_coe_ideal' FractionalIdeal.coeIdeal_le_coeIdeal'ₓ'. -/
+theorem coeIdeal_le_coeIdeal' [IsLocalization S P] (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
     (I : FractionalIdeal S P) ≤ J ↔ I ≤ J :=
   coeSubmodule_le_coeSubmodule h
-#align fractional_ideal.coe_ideal_le_coe_ideal' FractionalIdeal.coe_ideal_le_coe_ideal'
-
+#align fractional_ideal.coe_ideal_le_coe_ideal' FractionalIdeal.coeIdeal_le_coeIdeal'
+
+/- warning: fractional_ideal.coe_ideal_le_coe_ideal -> FractionalIdeal.coeIdeal_le_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (K : Type.{u2}) [_inst_4 : CommRing.{u2} K] [_inst_5 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K _inst_4))] [_inst_6 : IsFractionRing.{u1, u2} R _inst_1 K _inst_4 _inst_5] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) K (FractionalIdeal.setLike.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5)))) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5))) I) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K _inst_4 _inst_5))) J)) (LE.le.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) I J)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (K : Type.{u2}) [_inst_4 : CommRing.{u2} K] [_inst_5 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K _inst_4))] [_inst_6 : IsFractionRing.{u1, u2} R _inst_1 K _inst_4 _inst_5] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {J : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) K _inst_4 _inst_5) (Preorder.toLE.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) K _inst_4 _inst_5) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) K _inst_4 _inst_5) (SetLike.instPartialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) K _inst_4 _inst_5) K (FractionalIdeal.instSetLikeFractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) K _inst_4 _inst_5)))) (FractionalIdeal.coeIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) K _inst_4 _inst_5 I) (FractionalIdeal.coeIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) K _inst_4 _inst_5 J)) (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I J)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_le_coe_ideal FractionalIdeal.coeIdeal_le_coeIdealₓ'. -/
 @[simp]
-theorem coe_ideal_le_coe_ideal (K : Type _) [CommRing K] [Algebra R K] [IsFractionRing R K]
+theorem coeIdeal_le_coeIdeal (K : Type _) [CommRing K] [Algebra R K] [IsFractionRing R K]
     {I J : Ideal R} : (I : FractionalIdeal R⁰ K) ≤ J ↔ I ≤ J :=
   IsFractionRing.coeSubmodule_le_coeSubmodule
-#align fractional_ideal.coe_ideal_le_coe_ideal FractionalIdeal.coe_ideal_le_coe_ideal
+#align fractional_ideal.coe_ideal_le_coe_ideal FractionalIdeal.coeIdeal_le_coeIdeal
 
 instance : Zero (FractionalIdeal S P) :=
   ⟨(0 : Ideal R)⟩
 
+/- warning: fractional_ideal.mem_zero_iff -> FractionalIdeal.mem_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {x : P}, Iff (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (Eq.{succ u2} P x (OfNat.ofNat.{u2} P 0 (OfNat.mk.{u2} P 0 (Zero.zero.{u2} P (MulZeroClass.toHasZero.{u2} P (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {x : P}, Iff (Membership.mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (Eq.{succ u2} P x (OfNat.ofNat.{u2} P 0 (Zero.toOfNat0.{u2} P (CommMonoidWithZero.toZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_zero_iff FractionalIdeal.mem_zero_iffₓ'. -/
 @[simp]
 theorem mem_zero_iff {x : P} : x ∈ (0 : FractionalIdeal S P) ↔ x = 0 :=
   ⟨fun ⟨x', x'_mem_zero, x'_eq_x⟩ =>
@@ -270,58 +373,112 @@ theorem mem_zero_iff {x : P} : x ∈ (0 : FractionalIdeal S P) ↔ x = 0 :=
 
 variable {S}
 
+/- warning: fractional_ideal.coe_zero -> FractionalIdeal.coe_zero is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_zero FractionalIdeal.coe_zeroₓ'. -/
 @[simp, norm_cast]
 theorem coe_zero : ↑(0 : FractionalIdeal S P) = (⊥ : Submodule R P) :=
   Submodule.ext fun _ => mem_zero_iff S
 #align fractional_ideal.coe_zero FractionalIdeal.coe_zero
 
+/- warning: fractional_ideal.coe_ideal_bot -> FractionalIdeal.coeIdeal_bot is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Bot.bot.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instBotSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_bot FractionalIdeal.coeIdeal_botₓ'. -/
 @[simp, norm_cast]
-theorem coe_ideal_bot : ((⊥ : Ideal R) : FractionalIdeal S P) = 0 :=
+theorem coeIdeal_bot : ((⊥ : Ideal R) : FractionalIdeal S P) = 0 :=
   rfl
-#align fractional_ideal.coe_ideal_bot FractionalIdeal.coe_ideal_bot
+#align fractional_ideal.coe_ideal_bot FractionalIdeal.coeIdeal_bot
 
 variable (P)
 
 include loc
 
+/- warning: fractional_ideal.exists_mem_to_map_eq -> FractionalIdeal.exists_mem_algebraMap_eq is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {x : R} {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Exists.{succ u1} R (fun (x' : R) => And (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x' I) (Eq.{succ u2} P (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (fun (_x : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) => R -> P) (RingHom.hasCoeToFun.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (algebraMap.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) x') (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (fun (_x : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) => R -> P) (RingHom.hasCoeToFun.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (algebraMap.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) x)))) (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) x I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} (P : Type.{u1}) [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {x : R} {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) x I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_mem_to_map_eq FractionalIdeal.exists_mem_algebraMap_eqₓ'. -/
 @[simp]
-theorem exists_mem_to_map_eq {x : R} {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
+theorem exists_mem_algebraMap_eq {x : R} {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (∃ x', x' ∈ I ∧ algebraMap R P x' = algebraMap R P x) ↔ x ∈ I :=
   ⟨fun ⟨x', hx', Eq⟩ => IsLocalization.injective _ h Eq ▸ hx', fun h => ⟨x, h, rfl⟩⟩
-#align fractional_ideal.exists_mem_to_map_eq FractionalIdeal.exists_mem_to_map_eq
+#align fractional_ideal.exists_mem_to_map_eq FractionalIdeal.exists_mem_algebraMap_eq
 
 variable {P}
 
-theorem coe_ideal_injective' (h : S ≤ nonZeroDivisors R) :
+/- warning: fractional_ideal.coe_ideal_injective' -> FractionalIdeal.coeIdeal_injective' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Function.Injective.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) S (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Function.Injective.{succ u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (fun (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_injective' FractionalIdeal.coeIdeal_injective'ₓ'. -/
+theorem coeIdeal_injective' (h : S ≤ nonZeroDivisors R) :
     Function.Injective (coe : Ideal R → FractionalIdeal S P) := fun _ _ h' =>
-  ((coe_ideal_le_coe_ideal' S h).mp h'.le).antisymm ((coe_ideal_le_coe_ideal' S h).mp h'.ge)
-#align fractional_ideal.coe_ideal_injective' FractionalIdeal.coe_ideal_injective'
-
-theorem coe_ideal_inj' (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
+  ((coeIdeal_le_coeIdeal' S h).mp h'.le).antisymm ((coeIdeal_le_coeIdeal' S h).mp h'.ge)
+#align fractional_ideal.coe_ideal_injective' FractionalIdeal.coeIdeal_injective'
+
+/- warning: fractional_ideal.coe_ideal_inj' -> FractionalIdeal.coeIdeal_inj' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3], (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (forall {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) J)) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3], (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) S (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (forall {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {J : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, Iff (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J)) (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) I J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_inj' FractionalIdeal.coeIdeal_inj'ₓ'. -/
+theorem coeIdeal_inj' (h : S ≤ nonZeroDivisors R) {I J : Ideal R} :
     (I : FractionalIdeal S P) = J ↔ I = J :=
-  (coe_ideal_injective' h).eq_iff
-#align fractional_ideal.coe_ideal_inj' FractionalIdeal.coe_ideal_inj'
-
+  (coeIdeal_injective' h).eq_iff
+#align fractional_ideal.coe_ideal_inj' FractionalIdeal.coeIdeal_inj'
+
+/- warning: fractional_ideal.coe_ideal_eq_zero' -> FractionalIdeal.coeIdeal_eq_zero' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) S (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Iff (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) I (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_eq_zero' FractionalIdeal.coeIdeal_eq_zero'ₓ'. -/
 @[simp]
-theorem coe_ideal_eq_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
+theorem coeIdeal_eq_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (I : FractionalIdeal S P) = 0 ↔ I = (⊥ : Ideal R) :=
-  coe_ideal_inj' h
-#align fractional_ideal.coe_ideal_eq_zero' FractionalIdeal.coe_ideal_eq_zero'
-
-theorem coe_ideal_ne_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
+  coeIdeal_inj' h
+#align fractional_ideal.coe_ideal_eq_zero' FractionalIdeal.coeIdeal_eq_zero'
+
+/- warning: fractional_ideal.coe_ideal_ne_zero' -> FractionalIdeal.coeIdeal_ne_zero' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Iff (Ne.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (Ne.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (LE.le.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Preorder.toLE.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (PartialOrder.toPreorder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))))) S (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) -> (Iff (Ne.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (Ne.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) I (Bot.bot.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.instBotSubmodule.{u2, u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_ne_zero' FractionalIdeal.coeIdeal_ne_zero'ₓ'. -/
+theorem coeIdeal_ne_zero' {I : Ideal R} (h : S ≤ nonZeroDivisors R) :
     (I : FractionalIdeal S P) ≠ 0 ↔ I ≠ (⊥ : Ideal R) :=
-  not_iff_not.mpr <| coe_ideal_eq_zero' h
-#align fractional_ideal.coe_ideal_ne_zero' FractionalIdeal.coe_ideal_ne_zero'
+  not_iff_not.mpr <| coeIdeal_eq_zero' h
+#align fractional_ideal.coe_ideal_ne_zero' FractionalIdeal.coeIdeal_ne_zero'
 
 omit loc
 
-theorem coe_to_submodule_eq_bot {I : FractionalIdeal S P} : (I : Submodule R P) = ⊥ ↔ I = 0 :=
-  ⟨fun h => coe_to_submodule_injective (by simp [h]), fun h => by simp [h]⟩
-#align fractional_ideal.coe_to_submodule_eq_bot FractionalIdeal.coe_to_submodule_eq_bot
-
-theorem coe_to_submodule_ne_bot {I : FractionalIdeal S P} : ↑I ≠ (⊥ : Submodule R P) ↔ I ≠ 0 :=
-  not_iff_not.mpr coe_to_submodule_eq_bot
-#align fractional_ideal.coe_to_submodule_ne_bot FractionalIdeal.coe_to_submodule_ne_bot
+/- warning: fractional_ideal.coe_to_submodule_eq_bot -> FractionalIdeal.coeToSubmodule_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) (Bot.bot.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.hasBot.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))) (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (Bot.bot.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.instBotSubmodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_to_submodule_eq_bot FractionalIdeal.coeToSubmodule_eq_botₓ'. -/
+theorem coeToSubmodule_eq_bot {I : FractionalIdeal S P} : (I : Submodule R P) = ⊥ ↔ I = 0 :=
+  ⟨fun h => coeToSubmodule_injective (by simp [h]), fun h => by simp [h]⟩
+#align fractional_ideal.coe_to_submodule_eq_bot FractionalIdeal.coeToSubmodule_eq_bot
+
+/- warning: fractional_ideal.coe_to_submodule_ne_bot -> FractionalIdeal.coeToSubmodule_ne_bot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Ne.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) (Bot.bot.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.hasBot.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))) (Ne.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (Ne.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (Bot.bot.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.instBotSubmodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) (Ne.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_to_submodule_ne_bot FractionalIdeal.coeToSubmodule_ne_botₓ'. -/
+theorem coeToSubmodule_ne_bot {I : FractionalIdeal S P} : ↑I ≠ (⊥ : Submodule R P) ↔ I ≠ 0 :=
+  not_iff_not.mpr coeToSubmodule_eq_bot
+#align fractional_ideal.coe_to_submodule_ne_bot FractionalIdeal.coeToSubmodule_ne_bot
 
 instance : Inhabited (FractionalIdeal S P) :=
   ⟨0⟩
@@ -331,25 +488,55 @@ instance : One (FractionalIdeal S P) :=
 
 variable (S)
 
+/- warning: fractional_ideal.coe_ideal_top -> FractionalIdeal.coeIdeal_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_top FractionalIdeal.coeIdeal_topₓ'. -/
 @[simp, norm_cast]
-theorem coe_ideal_top : ((⊤ : Ideal R) : FractionalIdeal S P) = 1 :=
+theorem coeIdeal_top : ((⊤ : Ideal R) : FractionalIdeal S P) = 1 :=
   rfl
-#align fractional_ideal.coe_ideal_top FractionalIdeal.coe_ideal_top
-
+#align fractional_ideal.coe_ideal_top FractionalIdeal.coeIdeal_top
+
+/- warning: fractional_ideal.mem_one_iff -> FractionalIdeal.mem_one_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_one_iff FractionalIdeal.mem_one_iffₓ'. -/
 theorem mem_one_iff {x : P} : x ∈ (1 : FractionalIdeal S P) ↔ ∃ x' : R, algebraMap R P x' = x :=
   Iff.intro (fun ⟨x', _, h⟩ => ⟨x', h⟩) fun ⟨x', h⟩ => ⟨x', ⟨⟩, h⟩
 #align fractional_ideal.mem_one_iff FractionalIdeal.mem_one_iff
 
+/- warning: fractional_ideal.coe_mem_one -> FractionalIdeal.coe_mem_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_mem_one FractionalIdeal.coe_mem_oneₓ'. -/
 theorem coe_mem_one (x : R) : algebraMap R P x ∈ (1 : FractionalIdeal S P) :=
   (mem_one_iff S).mpr ⟨x, rfl⟩
 #align fractional_ideal.coe_mem_one FractionalIdeal.coe_mem_one
 
+/- warning: fractional_ideal.one_mem_one -> FractionalIdeal.one_mem_one is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (OfNat.ofNat.{u2} P 1 (OfNat.mk.{u2} P 1 (One.one.{u2} P (AddMonoidWithOne.toOne.{u2} P (AddGroupWithOne.toAddMonoidWithOne.{u2} P (AddCommGroupWithOne.toAddGroupWithOne.{u2} P (Ring.toAddCommGroupWithOne.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], Membership.mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (OfNat.ofNat.{u2} P 1 (One.toOfNat1.{u2} P (Semiring.toOne.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.one_mem_one FractionalIdeal.one_mem_oneₓ'. -/
 theorem one_mem_one : (1 : P) ∈ (1 : FractionalIdeal S P) :=
   (mem_one_iff S).mpr ⟨1, RingHom.map_one _⟩
 #align fractional_ideal.one_mem_one FractionalIdeal.one_mem_one
 
 variable {S}
 
+/- warning: fractional_ideal.coe_one_eq_coe_submodule_top -> FractionalIdeal.coe_one_eq_coeSubmodule_top is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (IsLocalization.coeSubmodule.{u1, u2} R _inst_1 P _inst_2 _inst_3 (Top.top.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasTop.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], Eq.{succ u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (IsLocalization.coeSubmodule.{u1, u2} R _inst_1 P _inst_2 _inst_3 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_one_eq_coe_submodule_top FractionalIdeal.coe_one_eq_coeSubmodule_topₓ'. -/
 /-- `(1 : fractional_ideal S P)` is defined as the R-submodule `f(R) ≤ P`.
 
 However, this is not definitionally equal to `1 : submodule R P`,
@@ -358,6 +545,12 @@ theorem coe_one_eq_coeSubmodule_top : ↑(1 : FractionalIdeal S P) = coeSubmodul
   rfl
 #align fractional_ideal.coe_one_eq_coe_submodule_top FractionalIdeal.coe_one_eq_coeSubmodule_top
 
+/- warning: fractional_ideal.coe_one -> FractionalIdeal.coe_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.one.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], Eq.{succ u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Submodule.one.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_one FractionalIdeal.coe_oneₓ'. -/
 @[simp, norm_cast]
 theorem coe_one : (↑(1 : FractionalIdeal S P) : Submodule R P) = 1 := by
   rw [coe_one_eq_coe_submodule_top, coe_submodule_top]
@@ -373,12 +566,24 @@ and ports the lattice structure on submodules to fractional ideals.
 -/
 
 
+/- warning: fractional_ideal.coe_le_coe -> FractionalIdeal.coe_le_coe is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) P (Submodule.setLike.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J)) (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I J)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J)) (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) I J)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_le_coe FractionalIdeal.coe_le_coeₓ'. -/
 @[simp]
 theorem coe_le_coe {I J : FractionalIdeal S P} :
     (I : Submodule R P) ≤ (J : Submodule R P) ↔ I ≤ J :=
   Iff.rfl
 #align fractional_ideal.coe_le_coe FractionalIdeal.coe_le_coe
 
+/- warning: fractional_ideal.zero_le -> FractionalIdeal.zero_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3))) I
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.zero_le FractionalIdeal.zero_leₓ'. -/
 theorem zero_le (I : FractionalIdeal S P) : 0 ≤ I :=
   by
   intro x hx
@@ -386,27 +591,57 @@ theorem zero_le (I : FractionalIdeal S P) : 0 ≤ I :=
   simpa using hx
 #align fractional_ideal.zero_le FractionalIdeal.zero_le
 
+/- warning: fractional_ideal.order_bot -> FractionalIdeal.orderBot is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], OrderBot.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], OrderBot.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.order_bot FractionalIdeal.orderBotₓ'. -/
 instance orderBot : OrderBot (FractionalIdeal S P)
     where
   bot := 0
   bot_le := zero_le
 #align fractional_ideal.order_bot FractionalIdeal.orderBot
 
+/- warning: fractional_ideal.bot_eq_zero -> FractionalIdeal.bot_eq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Bot.bot.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (OrderBot.toBot.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (FractionalIdeal.orderBot.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.bot_eq_zero FractionalIdeal.bot_eq_zeroₓ'. -/
 @[simp]
 theorem bot_eq_zero : (⊥ : FractionalIdeal S P) = 0 :=
   rfl
 #align fractional_ideal.bot_eq_zero FractionalIdeal.bot_eq_zero
 
+/- warning: fractional_ideal.le_zero_iff -> FractionalIdeal.le_zero_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_zero_iff FractionalIdeal.le_zero_iffₓ'. -/
 @[simp]
 theorem le_zero_iff {I : FractionalIdeal S P} : I ≤ 0 ↔ I = 0 :=
   le_bot_iff
 #align fractional_ideal.le_zero_iff FractionalIdeal.le_zero_iff
 
+/- warning: fractional_ideal.eq_zero_iff -> FractionalIdeal.eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (forall (x : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x I) -> (Eq.{succ u2} P x (OfNat.ofNat.{u2} P 0 (OfNat.mk.{u2} P 0 (Zero.zero.{u2} P (MulZeroClass.toHasZero.{u2} P (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (forall (x : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) x I) -> (Eq.{succ u1} P x (OfNat.ofNat.{u1} P 0 (Zero.toOfNat0.{u1} P (CommMonoidWithZero.toZero.{u1} P (CommSemiring.toCommMonoidWithZero.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_zero_iff FractionalIdeal.eq_zero_iffₓ'. -/
 theorem eq_zero_iff {I : FractionalIdeal S P} : I = 0 ↔ ∀ x ∈ I, x = (0 : P) :=
   ⟨fun h x hx => by simpa [h, mem_zero_iff] using hx, fun h =>
     le_bot_iff.mp fun x hx => (mem_zero_iff S).mpr (h x hx)⟩
 #align fractional_ideal.eq_zero_iff FractionalIdeal.eq_zero_iff
 
+/- warning: is_fractional.sup -> IsFractional.sup is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)} {J : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)}, (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 J) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Sup.sup.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemilatticeSup.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))) I J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)} {J : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)}, (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (Sup.sup.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemCommSemiring.toSemilatticeSup.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3))) I J))
+Case conversion may be inaccurate. Consider using '#align is_fractional.sup IsFractional.supₓ'. -/
 theorem IsFractional.sup {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I ⊔ J)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
@@ -421,6 +656,12 @@ theorem IsFractional.sup {I J : Submodule R P} :
         exact is_integer_smul (hJ bJ hbJ)⟩
 #align is_fractional.sup IsFractional.sup
 
+/- warning: is_fractional.inf_right -> IsFractional.inf_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)}, (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) -> (forall (J : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)), IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Inf.inf.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.hasInf.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) I J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)}, (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) -> (forall (J : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)), IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (Inf.inf.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.instInfSubmodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) I J))
+Case conversion may be inaccurate. Consider using '#align is_fractional.inf_right IsFractional.inf_rightₓ'. -/
 theorem IsFractional.inf_right {I : Submodule R P} : IsFractional S I → ∀ J, IsFractional S (I ⊓ J)
   | ⟨aI, haI, hI⟩, J =>
     ⟨aI, haI, fun b hb => by
@@ -431,6 +672,12 @@ theorem IsFractional.inf_right {I : Submodule R P} : IsFractional S I → ∀ J,
 instance : Inf (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊓ J, I.IsFractional.inf_right J⟩⟩
 
+/- warning: fractional_ideal.coe_inf -> FractionalIdeal.coe_inf is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : 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(Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (Inf.inf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instInfFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I J)) (Inf.inf.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.instInfSubmodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_inf FractionalIdeal.coe_infₓ'. -/
 @[simp, norm_cast]
 theorem coe_inf (I J : FractionalIdeal S P) : ↑(I ⊓ J) = (I ⊓ J : Submodule R P) :=
   rfl
@@ -439,14 +686,22 @@ theorem coe_inf (I J : FractionalIdeal S P) : ↑(I ⊓ J) = (I ⊓ J : Submodul
 instance : Sup (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊔ J, I.IsFractional.sup J.IsFractional⟩⟩
 
+/- warning: fractional_ideal.coe_sup -> FractionalIdeal.coe_sup is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : 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(CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemilatticeSup.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (Sup.sup.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instSupFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I J)) (Sup.sup.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (SemilatticeSup.toSup.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemCommSemiring.toSemilatticeSup.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3))) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_sup FractionalIdeal.coe_supₓ'. -/
 @[norm_cast]
 theorem coe_sup (I J : FractionalIdeal S P) : ↑(I ⊔ J) = (I ⊔ J : Submodule R P) :=
   rfl
 #align fractional_ideal.coe_sup FractionalIdeal.coe_sup
 
+#print FractionalIdeal.lattice /-
 instance lattice : Lattice (FractionalIdeal S P) :=
   Function.Injective.lattice _ Subtype.coe_injective coe_sup coe_inf
 #align fractional_ideal.lattice FractionalIdeal.lattice
+-/
 
 instance : SemilatticeSup (FractionalIdeal S P) :=
   { FractionalIdeal.lattice with }
@@ -458,21 +713,45 @@ section Semiring
 instance : Add (FractionalIdeal S P) :=
   ⟨(· ⊔ ·)⟩
 
+/- warning: fractional_ideal.sup_eq_add -> FractionalIdeal.sup_eq_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Sup.sup.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasSup.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I J) (HAdd.hAdd.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I J)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Sup.sup.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instSupFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I J) (HAdd.hAdd.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.sup_eq_add FractionalIdeal.sup_eq_addₓ'. -/
 @[simp]
 theorem sup_eq_add (I J : FractionalIdeal S P) : I ⊔ J = I + J :=
   rfl
 #align fractional_ideal.sup_eq_add FractionalIdeal.sup_eq_add
 
+/- warning: fractional_ideal.coe_add -> FractionalIdeal.coe_add is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (HAdd.hAdd.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I J)) (HAdd.hAdd.{u2, u2, u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (instHAdd.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Distrib.toHasAdd.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HAdd.hAdd.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J)) (HAdd.hAdd.{u1, u1, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHAdd.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Distrib.toAdd.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3))))))) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_add FractionalIdeal.coe_addₓ'. -/
 @[simp, norm_cast]
 theorem coe_add (I J : FractionalIdeal S P) : (↑(I + J) : Submodule R P) = I + J :=
   rfl
 #align fractional_ideal.coe_add FractionalIdeal.coe_add
 
+/- warning: fractional_ideal.coe_ideal_sup -> FractionalIdeal.coeIdeal_sup is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (Sup.sup.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemilatticeSup.toHasSup.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemilatticeSup.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) I J)) (HAdd.hAdd.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (J : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))), Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (Sup.sup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (SemilatticeSup.toSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemCommSemiring.toSemilatticeSup.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instIdemCommSemiringIdealToSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) I J)) (HAdd.hAdd.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_sup FractionalIdeal.coeIdeal_supₓ'. -/
 @[simp, norm_cast]
-theorem coe_ideal_sup (I J : Ideal R) : ↑(I ⊔ J) = (I + J : FractionalIdeal S P) :=
-  coe_to_submodule_injective <| coeSubmodule_sup _ _ _
-#align fractional_ideal.coe_ideal_sup FractionalIdeal.coe_ideal_sup
-
+theorem coeIdeal_sup (I J : Ideal R) : ↑(I ⊔ J) = (I + J : FractionalIdeal S P) :=
+  coeToSubmodule_injective <| coeSubmodule_sup _ _ _
+#align fractional_ideal.coe_ideal_sup FractionalIdeal.coeIdeal_sup
+
+/- warning: is_fractional.nsmul -> IsFractional.nsmul is a dubious translation:
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_inst_3 I) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HSMul.hSMul.{0, u1, u1} Nat (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHSMul.{0, u1} Nat (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (AddMonoid.SMul.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (AddMonoidWithOne.toAddMonoid.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))))) n I))
+Case conversion may be inaccurate. Consider using '#align is_fractional.nsmul IsFractional.nsmulₓ'. -/
 theorem IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
   | 0, _ => by
@@ -486,11 +765,23 @@ theorem IsFractional.nsmul {I : Submodule R P} :
 
 instance : SMul ℕ (FractionalIdeal S P) where smul n I := ⟨n • I, I.IsFractional.nsmul n⟩
 
+/- warning: fractional_ideal.coe_nsmul -> FractionalIdeal.coe_nsmul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (n : Nat) (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ 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_inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (SMul.smul.{0, u2} Nat (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasSmul.{u1, u2} R _inst_1 S P _inst_2 _inst_3) n I)) (SMul.smul.{0, u2} Nat (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (AddMonoid.SMul.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (AddMonoidWithOne.toAddMonoid.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))))) n ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (n : Nat) (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HSMul.hSMul.{0, u1, u1} Nat (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHSMul.{0, u1} Nat (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instSMulNatFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) n I)) (HSMul.hSMul.{0, u1, u1} Nat (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHSMul.{0, u1} Nat (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (AddMonoid.SMul.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (AddMonoidWithOne.toAddMonoid.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))))) n (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_nsmul FractionalIdeal.coe_nsmulₓ'. -/
 @[norm_cast]
 theorem coe_nsmul (n : ℕ) (I : FractionalIdeal S P) : (↑(n • I) : Submodule R P) = n • I :=
   rfl
 #align fractional_ideal.coe_nsmul FractionalIdeal.coe_nsmul
 
+/- warning: is_fractional.mul -> IsFractional.mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)} {J : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)}, (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 J) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.mul.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) I J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)} {J : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)}, (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HMul.hMul.{u1, u1, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHMul.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.mul.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) I J))
+Case conversion may be inaccurate. Consider using '#align is_fractional.mul IsFractional.mulₓ'. -/
 theorem IsFractional.mul {I J : Submodule R P} :
     IsFractional S I → IsFractional S J → IsFractional S (I * J : Submodule R P)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩ =>
@@ -507,12 +798,19 @@ theorem IsFractional.mul {I J : Submodule R P} :
         apply is_integer_add hx hy⟩
 #align is_fractional.mul IsFractional.mul
 
+/- warning: is_fractional.pow -> IsFractional.pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)}, (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) -> (forall (n : Nat), IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) Nat (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))))) I n))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)}, (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) -> (forall (n : Nat), IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HPow.hPow.{u1, 0, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) Nat (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHPow.{u1, 0} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) Nat (Monoid.Pow.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) I n))
+Case conversion may be inaccurate. Consider using '#align is_fractional.pow IsFractional.powₓ'. -/
 theorem IsFractional.pow {I : Submodule R P} (h : IsFractional S I) :
     ∀ n : ℕ, IsFractional S (I ^ n : Submodule R P)
   | 0 => isFractional_of_le_one _ (pow_zero _).le
   | n + 1 => (pow_succ I n).symm ▸ h.mul (_root_.is_fractional.pow n)
 #align is_fractional.pow IsFractional.pow
 
+#print FractionalIdeal.mul /-
 /-- `fractional_ideal.mul` is the product of two fractional ideals,
 used to define the `has_mul` instance.
 
@@ -524,20 +822,39 @@ so by making definitions irreducible, we hope to avoid deep unfolds.
 irreducible_def mul (I J : FractionalIdeal S P) : FractionalIdeal S P :=
   ⟨I * J, I.IsFractional.mul J.IsFractional⟩
 #align fractional_ideal.mul FractionalIdeal.mul
+-/
 
 -- local attribute [semireducible] mul
 instance : Mul (FractionalIdeal S P) :=
   ⟨fun I J => mul I J⟩
 
+/- warning: fractional_ideal.mul_eq_mul -> FractionalIdeal.mul_eq_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.mul.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I J) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I J)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.mul.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I J) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_eq_mul FractionalIdeal.mul_eq_mulₓ'. -/
 @[simp]
 theorem mul_eq_mul (I J : FractionalIdeal S P) : mul I J = I * J :=
   rfl
 #align fractional_ideal.mul_eq_mul FractionalIdeal.mul_eq_mul
 
+/- warning: fractional_ideal.mul_def -> FractionalIdeal.mul_def is a dubious translation:
+lean 3 declaration is
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(CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J)) (IsFractional.mul.{u1, u2} R _inst_1 S P _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J) (FractionalIdeal.isFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.isFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 J)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J) (Subtype.mk.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (fun (I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) => IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (HMul.hMul.{u1, u1, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHMul.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.mul.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J)) (IsFractional.mul.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J) (FractionalIdeal.isFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.isFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 J)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_def FractionalIdeal.mul_defₓ'. -/
 theorem mul_def (I J : FractionalIdeal S P) : I * J = ⟨I * J, I.IsFractional.mul J.IsFractional⟩ :=
   by simp only [← mul_eq_mul, mul]
 #align fractional_ideal.mul_def FractionalIdeal.mul_def
 
+/- warning: fractional_ideal.coe_mul -> FractionalIdeal.coe_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I J)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.mul.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J)) (HMul.hMul.{u1, u1, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHMul.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.mul.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_mul FractionalIdeal.coe_mulₓ'. -/
 @[simp, norm_cast]
 theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I * J :=
   by
@@ -545,13 +862,25 @@ theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I *
   rfl
 #align fractional_ideal.coe_mul FractionalIdeal.coe_mul
 
+/- warning: fractional_ideal.coe_ideal_mul -> FractionalIdeal.coeIdeal_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (J : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))), Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HMul.hMul.{u2, u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHMul.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instMulIdealToSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) I J)) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_mul FractionalIdeal.coeIdeal_mulₓ'. -/
 @[simp, norm_cast]
-theorem coe_ideal_mul (I J : Ideal R) : (↑(I * J) : FractionalIdeal S P) = I * J :=
+theorem coeIdeal_mul (I J : Ideal R) : (↑(I * J) : FractionalIdeal S P) = I * J :=
   by
   simp only [mul_def]
   exact coe_to_submodule_injective (coe_submodule_mul _ _ _)
-#align fractional_ideal.coe_ideal_mul FractionalIdeal.coe_ideal_mul
-
+#align fractional_ideal.coe_ideal_mul FractionalIdeal.coeIdeal_mul
+
+/- warning: fractional_ideal.mul_left_mono -> FractionalIdeal.mul_left_mono is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Monotone.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Monotone.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) ((fun (x._@.Mathlib.RingTheory.FractionalIdeal._hyg.5095 : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (x._@.Mathlib.RingTheory.FractionalIdeal._hyg.5097 : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) => HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) x._@.Mathlib.RingTheory.FractionalIdeal._hyg.5095 x._@.Mathlib.RingTheory.FractionalIdeal._hyg.5097) I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_left_mono FractionalIdeal.mul_left_monoₓ'. -/
 theorem mul_left_mono (I : FractionalIdeal S P) : Monotone ((· * ·) I) :=
   by
   intro J J' h
@@ -559,6 +888,12 @@ theorem mul_left_mono (I : FractionalIdeal S P) : Monotone ((· * ·) I) :=
   exact mul_le.mpr fun x hx y hy => mul_mem_mul hx (h hy)
 #align fractional_ideal.mul_left_mono FractionalIdeal.mul_left_mono
 
+/- warning: fractional_ideal.mul_right_mono -> FractionalIdeal.mul_right_mono is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Monotone.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (fun (J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) => HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) J I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Monotone.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (fun (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) => HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) J I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_right_mono FractionalIdeal.mul_right_monoₓ'. -/
 theorem mul_right_mono (I : FractionalIdeal S P) : Monotone fun J => J * I :=
   by
   intro J J' h
@@ -566,12 +901,24 @@ theorem mul_right_mono (I : FractionalIdeal S P) : Monotone fun J => J * I :=
   exact mul_le.mpr fun x hx y hy => mul_mem_mul (h hx) hy
 #align fractional_ideal.mul_right_mono FractionalIdeal.mul_right_mono
 
+/- warning: fractional_ideal.mul_mem_mul -> FractionalIdeal.mul_mem_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {i : P} {j : P}, (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) i I) -> (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) j J) -> (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) i j) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {i : P} {j : P}, (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) i I) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) j J) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) i j) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_mem_mul FractionalIdeal.mul_mem_mulₓ'. -/
 theorem mul_mem_mul {I J : FractionalIdeal S P} {i j : P} (hi : i ∈ I) (hj : j ∈ J) :
     i * j ∈ I * J := by
   simp only [mul_def]
   exact Submodule.mul_mem_mul hi hj
 #align fractional_ideal.mul_mem_mul FractionalIdeal.mul_mem_mul
 
+/- warning: fractional_ideal.mul_le -> FractionalIdeal.mul_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {K : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I J) K) (forall (i : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) i I) -> (forall (j : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) j J) -> (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) i j) K)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {K : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J) K) (forall (i : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) i I) -> (forall (j : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) j J) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) i j) K)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_le FractionalIdeal.mul_leₓ'. -/
 theorem mul_le {I J K : FractionalIdeal S P} : I * J ≤ K ↔ ∀ i ∈ I, ∀ j ∈ J, i * j ∈ K :=
   by
   simp only [mul_def]
@@ -581,11 +928,23 @@ theorem mul_le {I J K : FractionalIdeal S P} : I * J ≤ K ↔ ∀ i ∈ I, ∀
 instance : Pow (FractionalIdeal S P) ℕ :=
   ⟨fun I n => ⟨I ^ n, I.IsFractional.pow n⟩⟩
 
+/- warning: fractional_ideal.coe_pow -> FractionalIdeal.coe_pow is a dubious translation:
+lean 3 declaration is
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(CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) n)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (n : Nat), Eq.{succ u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HPow.hPow.{u1, 0, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) Nat (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHPow.{u1, 0} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) Nat (FractionalIdeal.instPowFractionalIdealNat.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I n)) (HPow.hPow.{u1, 0, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) Nat (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (instHPow.{u1, 0} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) Nat (Monoid.Pow.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) n)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_pow FractionalIdeal.coe_powₓ'. -/
 @[simp, norm_cast]
 theorem coe_pow (I : FractionalIdeal S P) (n : ℕ) : ↑(I ^ n) = (I ^ n : Submodule R P) :=
   rfl
 #align fractional_ideal.coe_pow FractionalIdeal.coe_pow
 
+/- warning: fractional_ideal.mul_induction_on -> FractionalIdeal.mul_induction_on is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {C : P -> Prop} {r : P}, (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) r (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I J)) -> (forall (i : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) i I) -> (forall (j : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) j J) -> (C (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) i j)))) -> (forall (x : P) (y : P), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} P P P (instHAdd.{u2} P (Distrib.toHasAdd.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) x y))) -> (C r)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {C : P -> Prop} {r : P}, (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) r (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J)) -> (forall (i : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) i I) -> (forall (j : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) j J) -> (C (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) i j)))) -> (forall (x : P) (y : P), (C x) -> (C y) -> (C (HAdd.hAdd.{u1, u1, u1} P P P (instHAdd.{u1} P (Distrib.toAdd.{u1} P (NonUnitalNonAssocSemiring.toDistrib.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))))) x y))) -> (C r)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_induction_on FractionalIdeal.mul_induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop} {r : P}
     (hr : r ∈ I * J) (hm : ∀ i ∈ I, ∀ j ∈ J, C (i * j)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
@@ -597,6 +956,12 @@ protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop}
 instance : NatCast (FractionalIdeal S P) :=
   ⟨Nat.unaryCast⟩
 
+/- warning: fractional_ideal.coe_nat_cast -> FractionalIdeal.coe_nat_cast is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{1, succ u2} Nat (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{1, succ u2} Nat (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Nat.castCoe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasNatCast.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) n)) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{1, succ u2} Nat (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{1, succ u2} Nat (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Nat.castCoe.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (AddMonoidWithOne.toNatCast.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))))))) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.coeToSubmodule.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Nat.cast.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instNatCastFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) n)) (Nat.cast.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Semiring.toNatCast.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))) n)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_castₓ'. -/
 theorem coe_nat_cast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
   show ↑n.unaryCast = ↑n by induction n <;> simp [*, Nat.unaryCast]
 #align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_cast
@@ -607,6 +972,12 @@ instance : CommSemiring (FractionalIdeal S P) :=
 
 variable (S P)
 
+/- warning: fractional_ideal.coe_submodule_hom -> FractionalIdeal.coeSubmoduleHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], RingHom.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], RingHom.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Semiring.toNonAssocSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Submodule.idemSemiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_submodule_hom FractionalIdeal.coeSubmoduleHomₓ'. -/
 /-- `fractional_ideal.submodule.has_coe` as a bundled `ring_hom`. -/
 @[simps]
 def coeSubmoduleHom : FractionalIdeal S P →+* Submodule R P :=
@@ -617,34 +988,70 @@ variable {S P}
 
 section Order
 
+/- warning: fractional_ideal.add_le_add_left -> FractionalIdeal.add_le_add_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I J) -> (forall (J' : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (HAdd.hAdd.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) J' I) (HAdd.hAdd.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) J' J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) I J) -> (forall (J' : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (HAdd.hAdd.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) J' I) (HAdd.hAdd.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) J' J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.add_le_add_left FractionalIdeal.add_le_add_leftₓ'. -/
 theorem add_le_add_left {I J : FractionalIdeal S P} (hIJ : I ≤ J) (J' : FractionalIdeal S P) :
     J' + I ≤ J' + J :=
   sup_le_sup_left hIJ J'
 #align fractional_ideal.add_le_add_left FractionalIdeal.add_le_add_left
 
+/- warning: fractional_ideal.mul_le_mul_left -> FractionalIdeal.mul_le_mul_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I J) -> (forall (J' : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) J' I) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) J' J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) I J) -> (forall (J' : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) J' I) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) J' J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_le_mul_left FractionalIdeal.mul_le_mul_leftₓ'. -/
 theorem mul_le_mul_left {I J : FractionalIdeal S P} (hIJ : I ≤ J) (J' : FractionalIdeal S P) :
     J' * I ≤ J' * J :=
   mul_le.mpr fun k hk j hj => mul_mem_mul hk (hIJ hj)
 #align fractional_ideal.mul_le_mul_left FractionalIdeal.mul_le_mul_left
 
+/- warning: fractional_ideal.le_self_mul_self -> FractionalIdeal.le_self_mul_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) -> (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3))) I) -> (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) I (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_self_mul_self FractionalIdeal.le_self_mul_selfₓ'. -/
 theorem le_self_mul_self {I : FractionalIdeal S P} (hI : 1 ≤ I) : I ≤ I * I :=
   by
   convert mul_left_mono I hI
   exact (mul_one I).symm
 #align fractional_ideal.le_self_mul_self FractionalIdeal.le_self_mul_self
 
+/- warning: fractional_ideal.mul_self_le_self -> FractionalIdeal.mul_self_le_self is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) -> (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) I I) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) -> (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I I) I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_self_le_self FractionalIdeal.mul_self_le_selfₓ'. -/
 theorem mul_self_le_self {I : FractionalIdeal S P} (hI : I ≤ 1) : I * I ≤ I :=
   by
   convert mul_left_mono I hI
   exact (mul_one I).symm
 #align fractional_ideal.mul_self_le_self FractionalIdeal.mul_self_le_self
 
-theorem coe_ideal_le_one {I : Ideal R} : (I : FractionalIdeal S P) ≤ 1 := fun x hx =>
-  let ⟨y, _, hy⟩ := (mem_coe_ideal S).mp hx
+/- warning: fractional_ideal.coe_ideal_le_one -> FractionalIdeal.coeIdeal_le_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_le_one FractionalIdeal.coeIdeal_le_oneₓ'. -/
+theorem coeIdeal_le_one {I : Ideal R} : (I : FractionalIdeal S P) ≤ 1 := fun x hx =>
+  let ⟨y, _, hy⟩ := (mem_coeIdeal S).mp hx
   (mem_one_iff S).mpr ⟨y, hy⟩
-#align fractional_ideal.coe_ideal_le_one FractionalIdeal.coe_ideal_le_one
-
-theorem le_one_iff_exists_coe_ideal {J : FractionalIdeal S P} :
+#align fractional_ideal.coe_ideal_le_one FractionalIdeal.coeIdeal_le_one
+
+/- warning: fractional_ideal.le_one_iff_exists_coe_ideal -> FractionalIdeal.le_one_iff_exists_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) J (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (Exists.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) J (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) (Exists.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_one_iff_exists_coe_ideal FractionalIdeal.le_one_iff_exists_coeIdealₓ'. -/
+theorem le_one_iff_exists_coeIdeal {J : FractionalIdeal S P} :
     J ≤ (1 : FractionalIdeal S P) ↔ ∃ I : Ideal R, ↑I = J :=
   by
   constructor
@@ -669,8 +1076,14 @@ theorem le_one_iff_exists_coe_ideal {J : FractionalIdeal S P} :
   · rintro ⟨I, hI⟩
     rw [← hI]
     apply coe_ideal_le_one
-#align fractional_ideal.le_one_iff_exists_coe_ideal FractionalIdeal.le_one_iff_exists_coe_ideal
-
+#align fractional_ideal.le_one_iff_exists_coe_ideal FractionalIdeal.le_one_iff_exists_coeIdeal
+
+/- warning: fractional_ideal.one_le -> FractionalIdeal.one_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (OfNat.ofNat.{u2} P 1 (OfNat.mk.{u2} P 1 (One.one.{u2} P (AddMonoidWithOne.toOne.{u2} P (AddGroupWithOne.toAddMonoidWithOne.{u2} P (AddCommGroupWithOne.toAddGroupWithOne.{u2} P (Ring.toAddCommGroupWithOne.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3))) I) (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (OfNat.ofNat.{u1} P 1 (One.toOfNat1.{u1} P (Semiring.toOne.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.one_le FractionalIdeal.one_leₓ'. -/
 @[simp]
 theorem one_le {I : FractionalIdeal S P} : 1 ≤ I ↔ (1 : P) ∈ I := by
   rw [← coe_le_coe, coe_one, Submodule.one_le, mem_coe]
@@ -678,28 +1091,46 @@ theorem one_le {I : FractionalIdeal S P} : 1 ≤ I ↔ (1 : P) ∈ I := by
 
 variable (S P)
 
+/- warning: fractional_ideal.coe_ideal_hom -> FractionalIdeal.coeIdealHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], RingHom.{u1, u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toNonAssocSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))], RingHom.{u1, u2} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toNonAssocSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toNonAssocSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_hom FractionalIdeal.coeIdealHomₓ'. -/
 /-- `coe_ideal_hom (S : submonoid R) P` is `coe : ideal R → fractional_ideal S P` as a ring hom -/
 @[simps]
 def coeIdealHom : Ideal R →+* FractionalIdeal S P
     where
   toFun := coe
-  map_add' := coe_ideal_sup
-  map_mul' := coe_ideal_mul
+  map_add' := coeIdeal_sup
+  map_mul' := coeIdeal_mul
   map_one' := by rw [Ideal.one_eq_top, coe_ideal_top]
-  map_zero' := coe_ideal_bot
+  map_zero' := coeIdeal_bot
 #align fractional_ideal.coe_ideal_hom FractionalIdeal.coeIdealHom
 
-theorem coe_ideal_pow (I : Ideal R) (n : ℕ) : (↑(I ^ n) : FractionalIdeal S P) = I ^ n :=
+/- warning: fractional_ideal.coe_ideal_pow -> FractionalIdeal.coeIdeal_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (n : Nat), Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHPow.{u1, 0} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.idemSemiring.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) I n)) (HPow.hPow.{u2, 0, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) Nat (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHPow.{u2, 0} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) Nat (FractionalIdeal.Nat.hasPow.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I) n)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (P : Type.{u1}) [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (n : Nat), Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.idemSemiring.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) I n)) (HPow.hPow.{u1, 0, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) Nat (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHPow.{u1, 0} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) Nat (FractionalIdeal.instPowFractionalIdealNat.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) n)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_pow FractionalIdeal.coeIdeal_powₓ'. -/
+theorem coeIdeal_pow (I : Ideal R) (n : ℕ) : (↑(I ^ n) : FractionalIdeal S P) = I ^ n :=
   (coeIdealHom S P).map_pow _ n
-#align fractional_ideal.coe_ideal_pow FractionalIdeal.coe_ideal_pow
+#align fractional_ideal.coe_ideal_pow FractionalIdeal.coeIdeal_pow
 
 open BigOperators
 
-theorem coe_ideal_finprod [IsLocalization S P] {α : Sort _} {f : α → Ideal R}
+/- warning: fractional_ideal.coe_ideal_finprod -> FractionalIdeal.coeIdeal_finprod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [_inst_4 : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {α : Sort.{u3}} {f : α -> (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))}, (LE.le.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Preorder.toHasLe.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (PartialOrder.toPreorder.{u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (SetLike.partialOrder.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) S (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) -> (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (finprod.{u1, u3} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) α (CommSemiring.toCommMonoid.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (IdemCommSemiring.toCommSemiring.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.idemCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (a : α) => f a))) (finprod.{u2, u3} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) α (CommSemiring.toCommMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (fun (a : α) => (fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) (f a))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] [_inst_4 : IsLocalization.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {α : Sort.{u1}} {f : α -> (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))}, (LE.le.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (Preorder.toLE.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (PartialOrder.toPreorder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (Submonoid.instCompleteLatticeSubmonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))))) S (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) -> (Eq.{succ u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3 (finprod.{u3, u1} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) α (CommSemiring.toCommMonoid.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (IdemCommSemiring.toCommSemiring.{u3} (Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Ideal.instIdemCommSemiringIdealToSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (fun (a : α) => f a))) (finprod.{u2, u1} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) α (CommSemiring.toCommMonoid.{u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)) (fun (a : α) => FractionalIdeal.coeIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3 (f a))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_finprod FractionalIdeal.coeIdeal_finprodₓ'. -/
+theorem coeIdeal_finprod [IsLocalization S P] {α : Sort _} {f : α → Ideal R}
     (hS : S ≤ nonZeroDivisors R) :
     ((∏ᶠ a : α, f a : Ideal R) : FractionalIdeal S P) = ∏ᶠ a : α, (f a : FractionalIdeal S P) :=
-  MonoidHom.map_finprod_of_injective (coeIdealHom S P).toMonoidHom (coe_ideal_injective' hS) f
-#align fractional_ideal.coe_ideal_finprod FractionalIdeal.coe_ideal_finprod
+  MonoidHom.map_finprod_of_injective (coeIdealHom S P).toMonoidHom (coeIdeal_injective' hS) f
+#align fractional_ideal.coe_ideal_finprod FractionalIdeal.coeIdeal_finprod
 
 end Order
 
@@ -707,6 +1138,12 @@ variable {P' : Type _} [CommRing P'] [Algebra R P'] [loc' : IsLocalization S P']
 
 variable {P'' : Type _} [CommRing P''] [Algebra R P''] [loc'' : IsLocalization S P'']
 
+/- warning: is_fractional.map -> IsFractional.map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] (g : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) {I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)}, (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I) -> (IsFractional.{u1, u3} R _inst_1 S P' _inst_4 _inst_5 (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R P P' (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} P' (NonUnitalNonAssocRing.toAddCommGroup.{u3} P' (NonAssocRing.toNonUnitalNonAssocRing.{u3} P' (Ring.toNonAssocRing.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) P P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R P P' (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgHom.toLinearMap.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5 g) I))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] (g : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) {I : Submodule.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)}, (IsFractional.{u3, u2} R _inst_1 S P _inst_2 _inst_3 I) -> (IsFractional.{u3, u1} R _inst_1 S P' _inst_4 _inst_5 (Submodule.map.{u3, u3, u2, u1, max u2 u1} R R P P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' 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(CommRing.toCommSemiring.{u3} R _inst_1)))) P P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (LinearMap.semilinearMapClass.{u3, u3, u2, u1} R R P P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (AlgHom.toLinearMap.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 g) I))
+Case conversion may be inaccurate. Consider using '#align is_fractional.map IsFractional.mapₓ'. -/
 theorem IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
     IsFractional S I → IsFractional S (Submodule.map g.toLinearMap I)
   | ⟨a, a_nonzero, hI⟩ =>
@@ -718,17 +1155,31 @@ theorem IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
       erw [← g.commutes, hx, g.map_smul, hb']⟩
 #align is_fractional.map IsFractional.map
 
+#print FractionalIdeal.map /-
 /-- `I.map g` is the pushforward of the fractional ideal `I` along the algebra morphism `g` -/
 def map (g : P →ₐ[R] P') : FractionalIdeal S P → FractionalIdeal S P' := fun I =>
   ⟨Submodule.map g.toLinearMap I, I.IsFractional.map g⟩
 #align fractional_ideal.map FractionalIdeal.map
+-/
 
+/- warning: fractional_ideal.coe_map -> FractionalIdeal.coe_map is a dubious translation:
+lean 3 declaration is
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(CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} P' (Semiring.toNonAssocSemiring.{u3} P' (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgHom.toLinearMap.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5 g) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] (g : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u1} (Submodule.{u3, u1} R P' 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(CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (RingHomSurjective.ids.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (LinearMap.{u3, u3, u2, u1} R R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) 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(CommRing.toCommSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (AlgHom.toLinearMap.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 g) (FractionalIdeal.coeToSubmodule.{u3, u2} R _inst_1 S P _inst_2 _inst_3 I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_map FractionalIdeal.coe_mapₓ'. -/
 @[simp, norm_cast]
 theorem coe_map (g : P →ₐ[R] P') (I : FractionalIdeal S P) :
     ↑(map g I) = Submodule.map g.toLinearMap I :=
   rfl
 #align fractional_ideal.coe_map FractionalIdeal.coe_map
 
+/- warning: fractional_ideal.mem_map -> FractionalIdeal.mem_map is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) g x) y)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_map FractionalIdeal.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {I : FractionalIdeal S P} {g : P →ₐ[R] P'} {y : P'} :
     y ∈ I.map g ↔ ∃ x, x ∈ I ∧ g x = y :=
@@ -737,18 +1188,32 @@ theorem mem_map {I : FractionalIdeal S P} {g : P →ₐ[R] P'} {y : P'} :
 
 variable (I J : FractionalIdeal S P) (g : P →ₐ[R] P')
 
+#print FractionalIdeal.map_id /-
 @[simp]
 theorem map_id : I.map (AlgHom.id _ _) = I :=
-  coe_to_submodule_injective (Submodule.map_id I)
+  coeToSubmodule_injective (Submodule.map_id I)
 #align fractional_ideal.map_id FractionalIdeal.map_id
+-/
 
+/- warning: fractional_ideal.map_comp -> FractionalIdeal.map_comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] {P'' : Type.{u4}} [_inst_6 : CommRing.{u4} P''] [_inst_7 : Algebra.{u1, u4} R P'' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} P'' (CommRing.toRing.{u4} P'' _inst_6))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (g : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) (g' : AlgHom.{u1, u3, u4} R P' P'' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) (Ring.toSemiring.{u4} P'' (CommRing.toRing.{u4} P'' _inst_6)) _inst_5 _inst_7), Eq.{succ u4} (FractionalIdeal.{u1, u4} R _inst_1 S P'' _inst_6 _inst_7) (FractionalIdeal.map.{u1, u2, u4} R _inst_1 S P _inst_2 _inst_3 P'' _inst_6 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R P P' P'' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) (Ring.toSemiring.{u4} P'' (CommRing.toRing.{u4} P'' _inst_6)) _inst_3 _inst_5 _inst_7 g' g) I) (FractionalIdeal.map.{u1, u3, u4} R _inst_1 S P' _inst_4 _inst_5 P'' _inst_6 _inst_7 g' (FractionalIdeal.map.{u1, u2, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I))
+but is expected to have type
+  forall {R : Type.{u4}} [_inst_1 : CommRing.{u4} R] {S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u4, u1} R P (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u4, u3} R P' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4))] {P'' : Type.{u2}} [_inst_6 : CommRing.{u2} P''] [_inst_7 : Algebra.{u4, u2} R P'' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} P'' (CommRing.toCommSemiring.{u2} P'' _inst_6))] (I : FractionalIdeal.{u4, u1} R _inst_1 S P _inst_2 _inst_3) (g : AlgHom.{u4, u1, u3} R P P' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4)) _inst_3 _inst_5) (g' : AlgHom.{u4, u3, u2} R P' P'' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4)) (CommSemiring.toSemiring.{u2} P'' (CommRing.toCommSemiring.{u2} P'' _inst_6)) _inst_5 _inst_7), Eq.{succ u2} (FractionalIdeal.{u4, u2} R _inst_1 S P'' _inst_6 _inst_7) (FractionalIdeal.map.{u4, u1, u2} R _inst_1 S P _inst_2 _inst_3 P'' _inst_6 _inst_7 (AlgHom.comp.{u4, u1, u3, u2} R P P' P'' (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4)) (CommSemiring.toSemiring.{u2} P'' (CommRing.toCommSemiring.{u2} P'' _inst_6)) _inst_3 _inst_5 _inst_7 g' g) I) (FractionalIdeal.map.{u4, u3, u2} R _inst_1 S P' _inst_4 _inst_5 P'' _inst_6 _inst_7 g' (FractionalIdeal.map.{u4, u1, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_comp FractionalIdeal.map_compₓ'. -/
 @[simp]
 theorem map_comp (g' : P' →ₐ[R] P'') : I.map (g'.comp g) = (I.map g).map g' :=
-  coe_to_submodule_injective (Submodule.map_comp g.toLinearMap g'.toLinearMap I)
+  coeToSubmodule_injective (Submodule.map_comp g.toLinearMap g'.toLinearMap I)
 #align fractional_ideal.map_comp FractionalIdeal.map_comp
 
+/- warning: fractional_ideal.map_coe_ideal -> FractionalIdeal.map_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] (g : AlgHom.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5) (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Eq.{succ u3} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.map.{u1, u2, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I)) ((fun (a : Type.{u1}) (b : Type.{u3}) [self : HasLiftT.{succ u1, succ u3} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (HasLiftT.mk.{succ u1, succ u3} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (CoeTCₓ.coe.{succ u1, succ u3} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasCoeT.{u1, u3} R _inst_1 S P' _inst_4 _inst_5))) I)
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u3, u1} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {P' : Type.{u2}} [_inst_4 : CommRing.{u2} P'] [_inst_5 : Algebra.{u3, u2} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P' (CommRing.toCommSemiring.{u2} P' _inst_4))] (g : AlgHom.{u3, u1, u2} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) (CommSemiring.toSemiring.{u2} P' (CommRing.toCommSemiring.{u2} P' _inst_4)) _inst_3 _inst_5) (I : Ideal.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))), Eq.{succ u2} (FractionalIdeal.{u3, u2} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.map.{u3, u1, u2} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g (FractionalIdeal.coeIdeal.{u3, u1} R _inst_1 S P _inst_2 _inst_3 I)) (FractionalIdeal.coeIdeal.{u3, u2} R _inst_1 S P' _inst_4 _inst_5 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_coe_ideal FractionalIdeal.map_coeIdealₓ'. -/
 @[simp, norm_cast]
-theorem map_coe_ideal (I : Ideal R) : (I : FractionalIdeal S P).map g = I :=
+theorem map_coeIdeal (I : Ideal R) : (I : FractionalIdeal S P).map g = I :=
   by
   ext x
   simp only [mem_coe_ideal]
@@ -757,23 +1222,47 @@ theorem map_coe_ideal (I : Ideal R) : (I : FractionalIdeal S P).map g = I :=
     exact ⟨y, hy, (g.commutes y).symm⟩
   · rintro ⟨y, hy, rfl⟩
     exact ⟨_, ⟨y, hy, rfl⟩, g.commutes y⟩
-#align fractional_ideal.map_coe_ideal FractionalIdeal.map_coe_ideal
-
+#align fractional_ideal.map_coe_ideal FractionalIdeal.map_coeIdeal
+
+/- warning: fractional_ideal.map_one -> FractionalIdeal.map_one is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_one FractionalIdeal.map_oneₓ'. -/
 @[simp]
 theorem map_one : (1 : FractionalIdeal S P).map g = 1 :=
-  map_coe_ideal g ⊤
+  map_coeIdeal g ⊤
 #align fractional_ideal.map_one FractionalIdeal.map_one
 
+/- warning: fractional_ideal.map_zero -> FractionalIdeal.map_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_zero FractionalIdeal.map_zeroₓ'. -/
 @[simp]
 theorem map_zero : (0 : FractionalIdeal S P).map g = 0 :=
-  map_coe_ideal g 0
+  map_coeIdeal g 0
 #align fractional_ideal.map_zero FractionalIdeal.map_zero
 
+/- warning: fractional_ideal.map_add -> FractionalIdeal.map_add is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u2, u3} R P' (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (g : AlgHom.{u2, u1, u3} R P P' (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4)) _inst_3 _inst_5), Eq.{succ u3} (FractionalIdeal.{u2, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.map.{u2, u1, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g (HAdd.hAdd.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHAdd.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J)) (HAdd.hAdd.{u3, u3, u3} (FractionalIdeal.{u2, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.{u2, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.{u2, u3} R _inst_1 S P' _inst_4 _inst_5) (instHAdd.{u3} (FractionalIdeal.{u2, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instAddFractionalIdeal.{u2, u3} R _inst_1 S P' _inst_4 _inst_5)) (FractionalIdeal.map.{u2, u1, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g I) (FractionalIdeal.map.{u2, u1, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_add FractionalIdeal.map_addₓ'. -/
 @[simp]
 theorem map_add : (I + J).map g = I.map g + J.map g :=
-  coe_to_submodule_injective (Submodule.map_sup _ _ _)
+  coeToSubmodule_injective (Submodule.map_sup _ _ _)
 #align fractional_ideal.map_add FractionalIdeal.map_add
 
+/- warning: fractional_ideal.map_mul -> FractionalIdeal.map_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_mul FractionalIdeal.map_mulₓ'. -/
 @[simp]
 theorem map_mul : (I * J).map g = I.map g * J.map g :=
   by
@@ -781,27 +1270,57 @@ theorem map_mul : (I * J).map g = I.map g * J.map g :=
   exact coe_to_submodule_injective (Submodule.map_mul _ _ _)
 #align fractional_ideal.map_mul FractionalIdeal.map_mul
 
+/- warning: fractional_ideal.map_map_symm -> FractionalIdeal.map_map_symm is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_map_symm FractionalIdeal.map_map_symmₓ'. -/
 @[simp]
 theorem map_map_symm (g : P ≃ₐ[R] P') : (I.map (g : P →ₐ[R] P')).map (g.symm : P' →ₐ[R] P) = I := by
   rw [← map_comp, g.symm_comp, map_id]
 #align fractional_ideal.map_map_symm FractionalIdeal.map_map_symm
 
+/- warning: fractional_ideal.map_symm_map -> FractionalIdeal.map_symm_map is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_symm_map FractionalIdeal.map_symm_mapₓ'. -/
 @[simp]
 theorem map_symm_map (I : FractionalIdeal S P') (g : P ≃ₐ[R] P') :
     (I.map (g.symm : P' →ₐ[R] P)).map (g : P →ₐ[R] P') = I := by
   rw [← map_comp, g.comp_symm, map_id]
 #align fractional_ideal.map_symm_map FractionalIdeal.map_symm_map
 
+/- warning: fractional_ideal.map_mem_map -> FractionalIdeal.map_mem_map is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u1}} [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] {f : AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5}, (Function.Injective.{succ u2, succ u1} P P' (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f)) -> (forall {x : P} {I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') x) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) P' (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) P (fun (_x : P) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : P) => P') _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (SMulZeroClass.toSMul.{u3, u2} R P (AddMonoid.toZero.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R P (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3))))) (SMulZeroClass.toSMul.{u3, u1} R P' (AddMonoid.toZero.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R P' (AddMonoid.toAddZeroClass.{u1} P' (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (DistribMulAction.toDistribSMul.{u3, u1} R P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} P' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) (Module.toDistribMulAction.{u3, u2} R P (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (Algebra.toModule.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f x) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f I)) (Membership.mem.{u2, u2} P (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)) x I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_mem_map FractionalIdeal.map_mem_mapₓ'. -/
 theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I : FractionalIdeal S P} :
     f x ∈ map f I ↔ x ∈ I :=
   mem_map.trans ⟨fun ⟨x', hx', x'_eq⟩ => h x'_eq ▸ hx', fun h => ⟨x, h, rfl⟩⟩
 #align fractional_ideal.map_mem_map FractionalIdeal.map_mem_map
 
+/- warning: fractional_ideal.map_injective -> FractionalIdeal.map_injective is a dubious translation:
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(CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) (Module.toDistribMulAction.{u3, u1} R P' (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (Algebra.toModule.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgHom.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgHom.algHomClass.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5))))) f)) -> (Function.Injective.{succ u2, succ u1} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 f))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_injective FractionalIdeal.map_injectiveₓ'. -/
 theorem map_injective (f : P →ₐ[R] P') (h : Function.Injective f) :
     Function.Injective (map f : FractionalIdeal S P → FractionalIdeal S P') := fun I J hIJ =>
   ext fun x => (map_mem_map h).symm.trans (hIJ.symm ▸ map_mem_map h)
 #align fractional_ideal.map_injective FractionalIdeal.map_injective
 
+/- warning: fractional_ideal.map_equiv -> FractionalIdeal.mapEquiv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4))], (AlgEquiv.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4)) _inst_3 _inst_5) -> (RingEquiv.{u2, u3} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instMulFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instAddFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_equiv FractionalIdeal.mapEquivₓ'. -/
 /-- If `g` is an equivalence, `map g` is an isomorphism -/
 def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S P'
     where
@@ -813,28 +1332,58 @@ def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S
   right_inv I := by rw [← map_comp, AlgEquiv.comp_symm, map_id]
 #align fractional_ideal.map_equiv FractionalIdeal.mapEquiv
 
+/- warning: fractional_ideal.coe_fun_map_equiv -> FractionalIdeal.coeFun_mapEquiv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coeFun_mapEquivₓ'. -/
 @[simp]
-theorem coe_fun_mapEquiv (g : P ≃ₐ[R] P') :
+theorem coeFun_mapEquiv (g : P ≃ₐ[R] P') :
     (mapEquiv g : FractionalIdeal S P → FractionalIdeal S P') = map g :=
   rfl
-#align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coe_fun_mapEquiv
-
+#align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coeFun_mapEquiv
+
+/- warning: fractional_ideal.map_equiv_apply -> FractionalIdeal.mapEquiv_apply is a dubious translation:
+lean 3 declaration is
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(FractionalIdeal.map.{u3, u2, u1} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 (AlgHomClass.toAlgHom.{u3, u2, u1, max u2 u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgEquiv.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5) R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} R P P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)) _inst_3 _inst_5)) g) I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_equiv_apply FractionalIdeal.mapEquiv_applyₓ'. -/
 @[simp]
 theorem mapEquiv_apply (g : P ≃ₐ[R] P') (I : FractionalIdeal S P) : mapEquiv g I = map (↑g) I :=
   rfl
 #align fractional_ideal.map_equiv_apply FractionalIdeal.mapEquiv_apply
 
+/- warning: fractional_ideal.map_equiv_symm -> FractionalIdeal.mapEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] {P' : Type.{u3}} [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] (g : AlgEquiv.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5), Eq.{max (succ u3) (succ u2)} (RingEquiv.{u3, u2} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasAdd.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (RingEquiv.symm.{u2, u3} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasAdd.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.mapEquiv.{u1, u2, u3} R _inst_1 S P _inst_2 _inst_3 P' _inst_4 _inst_5 g)) (FractionalIdeal.mapEquiv.{u1, u3, u2} R _inst_1 S P' _inst_4 _inst_5 P _inst_2 _inst_3 (AlgEquiv.symm.{u1, u2, u3} R P P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4)) _inst_3 _inst_5 g))
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_equiv_symm FractionalIdeal.mapEquiv_symmₓ'. -/
 @[simp]
 theorem mapEquiv_symm (g : P ≃ₐ[R] P') :
     ((mapEquiv g).symm : FractionalIdeal S P' ≃+* _) = mapEquiv g.symm :=
   rfl
 #align fractional_ideal.map_equiv_symm FractionalIdeal.mapEquiv_symm
 
+/- warning: fractional_ideal.map_equiv_refl -> FractionalIdeal.mapEquiv_refl is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_equiv_refl FractionalIdeal.mapEquiv_reflₓ'. -/
 @[simp]
 theorem mapEquiv_refl : mapEquiv AlgEquiv.refl = RingEquiv.refl (FractionalIdeal S P) :=
   RingEquiv.ext fun x => by simp
 #align fractional_ideal.map_equiv_refl FractionalIdeal.mapEquiv_refl
 
+/- warning: fractional_ideal.is_fractional_span_iff -> FractionalIdeal.isFractional_span_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] {s : Set.{u2} P}, Iff (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Submodule.span.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) s)) (Exists.{succ u1} R (fun (a : R) => And (Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) a S) (forall (b : P), (Membership.mem.{u2, u2} P (Set.{u2} P) (Set.instMembershipSet.{u2} P) b s) -> (IsLocalization.IsInteger.{u1, u2} R _inst_1 P _inst_2 _inst_3 (HSMul.hSMul.{u1, u2, u2} R P P (instHSMul.{u1, u2} R P (Algebra.toSMul.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3)) a b)))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_span_iff FractionalIdeal.isFractional_span_iffₓ'. -/
 theorem isFractional_span_iff {s : Set P} :
     IsFractional S (span R s) ↔ ∃ a ∈ S, ∀ b : P, b ∈ s → IsInteger R (a • b) :=
   ⟨fun ⟨a, a_mem, h⟩ => ⟨a, a_mem, fun b hb => h b (subset_span hb)⟩, fun ⟨a, a_mem, h⟩ =>
@@ -853,16 +1402,28 @@ theorem isFractional_span_iff {s : Set P} :
 
 include loc
 
-theorem isFractional_of_fG {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
+/- warning: fractional_ideal.is_fractional_of_fg -> FractionalIdeal.isFractional_of_fg is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {I : Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)}, (Submodule.FG.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) I) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {I : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)}, (Submodule.FG.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) I) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fgₓ'. -/
+theorem isFractional_of_fg {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
   by
   rcases hI with ⟨I, rfl⟩
   rcases exist_integer_multiples_of_finset S I with ⟨⟨s, hs1⟩, hs⟩
   rw [is_fractional_span_iff]
   exact ⟨s, hs1, hs⟩
-#align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fG
+#align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fg
 
 omit loc
 
+/- warning: fractional_ideal.mem_span_mul_finite_of_mem_mul -> FractionalIdeal.mem_span_mul_finite_of_mem_mul is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {x : P}, (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) x (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) I J)) -> (Exists.{succ u1} (Finset.{u1} P) (fun (T : Finset.{u1} P) => Exists.{succ u1} (Finset.{u1} P) (fun (T' : Finset.{u1} P) => And (HasSubset.Subset.{u1} (Set.{u1} P) (Set.instHasSubsetSet.{u1} P) (Finset.toSet.{u1} P T) (SetLike.coe.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I)) (And (HasSubset.Subset.{u1} (Set.{u1} P) (Set.instHasSubsetSet.{u1} P) (Finset.toSet.{u1} P T') (SetLike.coe.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) J)) (Membership.mem.{u1, u1} P (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) P (Submodule.setLike.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3))) x (Submodule.span.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (HMul.hMul.{u1, u1, u1} (Set.{u1} P) (Set.{u1} P) (Set.{u1} P) (instHMul.{u1} (Set.{u1} P) (Set.mul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2)))))) (Finset.toSet.{u1} P T) (Finset.toSet.{u1} P T'))))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_span_mul_finite_of_mem_mul FractionalIdeal.mem_span_mul_finite_of_mem_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx : x ∈ I * J) :
     ∃ T T' : Finset P, (T : Set P) ⊆ I ∧ (T' : Set P) ⊆ J ∧ x ∈ span R (T * T' : Set P) :=
   Submodule.mem_span_mul_finite_of_mem_mul (by simpa using mem_coe.mpr hx)
@@ -870,32 +1431,62 @@ theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx :
 
 variable (S)
 
-theorem coe_ideal_fG (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
+/- warning: fractional_ideal.coe_ideal_fg -> FractionalIdeal.coeIdeal_fg is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_fg FractionalIdeal.coeIdeal_fgₓ'. -/
+theorem coeIdeal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
     FG ((I : FractionalIdeal S P) : Submodule R P) ↔ I.FG :=
   coeSubmodule_fg _ inj _
-#align fractional_ideal.coe_ideal_fg FractionalIdeal.coe_ideal_fG
+#align fractional_ideal.coe_ideal_fg FractionalIdeal.coeIdeal_fg
 
 variable {S}
 
-theorem fG_unit (I : (FractionalIdeal S P)ˣ) : FG (I : Submodule R P) :=
+/- warning: fractional_ideal.fg_unit -> FractionalIdeal.fg_unit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : Units.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))), Submodule.FG.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Units.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (Units.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (Units.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeTrans.{succ u2, succ u2, succ u2} (Units.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (Units.hasCoe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))))))) I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] (I : Units.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3))))), Submodule.FG.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) (FractionalIdeal.coeToSubmodule.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Units.val.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.fg_unit FractionalIdeal.fg_unitₓ'. -/
+theorem fg_unit (I : (FractionalIdeal S P)ˣ) : FG (I : Submodule R P) :=
   Submodule.fg_unit <| Units.map (coeSubmoduleHom S P).toMonoidHom I
-#align fractional_ideal.fg_unit FractionalIdeal.fG_unit
-
-theorem fG_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : FG (I : Submodule R P) :=
-  fG_unit h.Unit
-#align fractional_ideal.fg_of_is_unit FractionalIdeal.fG_of_isUnit
-
-theorem Ideal.fG_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
+#align fractional_ideal.fg_unit FractionalIdeal.fg_unit
+
+/- warning: fractional_ideal.fg_of_is_unit -> FractionalIdeal.fg_of_isUnit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), (IsUnit.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) -> (Submodule.FG.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), (IsUnit.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)))) I) -> (Submodule.FG.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.fg_of_is_unit FractionalIdeal.fg_of_isUnitₓ'. -/
+theorem fg_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : FG (I : Submodule R P) :=
+  fg_unit h.Unit
+#align fractional_ideal.fg_of_is_unit FractionalIdeal.fg_of_isUnit
+
+/- warning: ideal.fg_of_is_unit -> Ideal.fg_of_isUnit is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))], (Function.Injective.{succ u1, succ u2} R P (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (fun (_x : RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) => R -> P) (RingHom.hasCoeToFun.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (algebraMap.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))) -> (forall (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (IsUnit.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Semiring.toMonoidWithZero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.commSemiring.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 S P _inst_2 _inst_3))) I)) -> (Ideal.FG.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) I))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ideal.fg_of_is_unit Ideal.fg_of_isUnitₓ'. -/
+theorem Ideal.fg_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
     (h : IsUnit (I : FractionalIdeal S P)) : I.FG :=
   by
   rw [← coe_ideal_fg S inj I]
   exact fg_of_is_unit I h
-#align ideal.fg_of_is_unit Ideal.fG_of_isUnit
+#align ideal.fg_of_is_unit Ideal.fg_of_isUnit
 
 variable (S P P')
 
 include loc loc'
 
+/- warning: fractional_ideal.canonical_equiv -> FractionalIdeal.canonicalEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (P' : Type.{u3}) [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] [loc' : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) S P' (CommRing.toCommSemiring.{u3} P' _inst_4) _inst_5], RingEquiv.{u2, u3} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasAdd.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasAdd.{u1, u3} R _inst_1 S P' _inst_4 _inst_5)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (P' : Type.{u3}) [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_4))] [loc' : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) S P' (CommRing.toCommSemiring.{u3} P' _inst_4) _inst_5], RingEquiv.{u2, u3} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instMulFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instAddFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv FractionalIdeal.canonicalEquivₓ'. -/
 /-- `canonical_equiv f f'` is the canonical equivalence between the fractional
 ideals in `P` and in `P'` -/
 noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* FractionalIdeal S P' :=
@@ -906,6 +1497,12 @@ noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* Fractio
       commutes' := fun r => ringEquivOfRingEquiv_eq _ _ }
 #align fractional_ideal.canonical_equiv FractionalIdeal.canonicalEquiv
 
+/- warning: fractional_ideal.mem_canonical_equiv_apply -> FractionalIdeal.mem_canonicalEquiv_apply is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] [loc : IsLocalization.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (P' : Type.{u1}) [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] [loc' : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S P' (CommRing.toCommSemiring.{u1} P' _inst_4) _inst_5] {I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3} {x : P'}, Iff 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_inst_2 _inst_3) (Semiring.toNonAssocSemiring.{u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (CommSemiring.toSemiring.{u2} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instCommSemiringFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (Semiring.toNonAssocSemiring.{u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instCommSemiringFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5)))) (RingEquiv.instRingEquivClassRingEquiv.{u2, u1} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instMulFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : P) => P') a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} P P' (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))) (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4)))) P P' (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} P' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P' (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} P P' (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))) (Semiring.toNonAssocSemiring.{u1} P' 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(Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))) (Semiring.toNonAssocSemiring.{u1} P' (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))))))) (IsLocalization.map.{u3, u2, u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3 R (CommRing.toCommSemiring.{u3} R _inst_1) loc S P' (CommRing.toCommSemiring.{u1} P' _inst_4) _inst_5 loc' (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (fun (y : R) (hy : Membership.mem.{u3, u3} R (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (SetLike.instMembership.{u3, u3} (Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R 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(Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) R R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (RingHom.instRingHomClassRingHom.{u3, u3} R R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) y) S) => this) hy])) y) x)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_canonical_equiv_apply FractionalIdeal.mem_canonicalEquiv_applyₓ'. -/
 @[simp]
 theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
     x ∈ canonicalEquiv S P P' I ↔
@@ -918,6 +1515,12 @@ theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
   exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
 #align fractional_ideal.mem_canonical_equiv_apply FractionalIdeal.mem_canonicalEquiv_apply
 
+/- warning: fractional_ideal.canonical_equiv_symm -> FractionalIdeal.canonicalEquiv_symm is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symmₓ'. -/
 @[simp]
 theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P' P :=
   RingEquiv.ext fun I =>
@@ -928,10 +1531,22 @@ theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P'
       exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
 #align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symm
 
+/- warning: fractional_ideal.canonical_equiv_flip -> FractionalIdeal.canonicalEquiv_flip is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flipₓ'. -/
 theorem canonicalEquiv_flip (I) : canonicalEquiv S P P' (canonicalEquiv S P' P I) = I := by
   rw [← canonical_equiv_symm, RingEquiv.symm_apply_apply]
 #align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flip
 
+/- warning: fractional_ideal.canonical_equiv_canonical_equiv -> FractionalIdeal.canonicalEquiv_canonicalEquiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (P' : Type.{u3}) [_inst_4 : CommRing.{u3} P'] [_inst_5 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_4))] [loc' : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) S P' (CommRing.toCommSemiring.{u3} P' _inst_4) _inst_5] (P'' : Type.{u4}) [_inst_8 : CommRing.{u4} P''] [_inst_9 : Algebra.{u1, u4} R P'' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} P'' (CommRing.toRing.{u4} P'' _inst_8))] [_inst_10 : IsLocalization.{u1, u4} R (CommRing.toCommSemiring.{u1} R _inst_1) S P'' (CommRing.toCommSemiring.{u4} P'' _inst_8) _inst_9] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u4} (FractionalIdeal.{u1, u4} R _inst_1 S P'' _inst_8 _inst_9) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingEquiv.{u3, u4} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.{u1, u4} R _inst_1 S P'' _inst_8 _inst_9) (FractionalIdeal.hasMul.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasAdd.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.hasMul.{u1, u4} R _inst_1 S P'' _inst_8 _inst_9) (FractionalIdeal.hasAdd.{u1, u4} R _inst_1 S P'' _inst_8 _inst_9)) (fun (_x : RingEquiv.{u3, u4} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.{u1, u4} R _inst_1 S P'' _inst_8 _inst_9) (FractionalIdeal.hasMul.{u1, u3} R _inst_1 S P' 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+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) (P : Type.{u2}) [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u3, u2} R P (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] [loc : IsLocalization.{u3, u2} R (CommRing.toCommSemiring.{u3} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (P' : Type.{u1}) [_inst_4 : CommRing.{u1} P'] [_inst_5 : Algebra.{u3, u1} R P' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} P' (CommRing.toCommSemiring.{u1} P' _inst_4))] [loc' : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S P' (CommRing.toCommSemiring.{u1} P' _inst_4) _inst_5] (P'' : Type.{u4}) [_inst_8 : CommRing.{u4} P''] [_inst_9 : Algebra.{u3, u4} R P'' (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} P'' (CommRing.toCommSemiring.{u4} P'' _inst_8))] [_inst_10 : IsLocalization.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) S P'' (CommRing.toCommSemiring.{u4} P'' _inst_8) _inst_9] (I : FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3), Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) => FractionalIdeal.{u3, u4} R _inst_1 S P'' _inst_8 _inst_9) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingEquiv.{u2, u1} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instMulFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u3, u1} R _inst_1 S P' _inst_4 _inst_5) (FractionalIdeal.instAddFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u3, u1} R _inst_1 S P' 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P'' _inst_8 _inst_9) (CommSemiring.toSemiring.{u4} (FractionalIdeal.{u3, u4} R _inst_1 S P'' _inst_8 _inst_9) (FractionalIdeal.instCommSemiringFractionalIdeal.{u3, u4} R _inst_1 S P'' _inst_8 _inst_9)))) (RingEquiv.instRingEquivClassRingEquiv.{u2, u4} (FractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u3, u4} R _inst_1 S P'' _inst_8 _inst_9) (FractionalIdeal.instMulFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u3, u4} R _inst_1 S P'' _inst_8 _inst_9) (FractionalIdeal.instAddFractionalIdeal.{u3, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instAddFractionalIdeal.{u3, u4} R _inst_1 S P'' _inst_8 _inst_9))))) (FractionalIdeal.canonicalEquiv.{u3, u2, u4} R _inst_1 S P _inst_2 _inst_3 loc P'' _inst_8 _inst_9 _inst_10) I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquivₓ'. -/
 @[simp]
 theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] (I : FractionalIdeal S P) :
@@ -943,21 +1558,39 @@ theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P
   rfl
 #align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquiv
 
+/- warning: fractional_ideal.canonical_equiv_trans_canonical_equiv -> FractionalIdeal.canonicalEquiv_trans_canonicalEquiv is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_trans_canonical_equiv FractionalIdeal.canonicalEquiv_trans_canonicalEquivₓ'. -/
 theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] :
     (canonicalEquiv S P P').trans (canonicalEquiv S P' P'') = canonicalEquiv S P P'' :=
   RingEquiv.ext (canonicalEquiv_canonicalEquiv S P P' P'')
 #align fractional_ideal.canonical_equiv_trans_canonical_equiv FractionalIdeal.canonicalEquiv_trans_canonicalEquiv
 
+/- warning: fractional_ideal.canonical_equiv_coe_ideal -> FractionalIdeal.canonicalEquiv_coeIdeal is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coeIdealₓ'. -/
 @[simp]
-theorem canonicalEquiv_coe_ideal (I : Ideal R) : canonicalEquiv S P P' I = I :=
+theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I :=
   by
   ext
   simp [IsLocalization.map_eq]
-#align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coe_ideal
+#align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coeIdeal
 
 omit loc'
 
+/- warning: fractional_ideal.canonical_equiv_self -> FractionalIdeal.canonicalEquiv_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_self FractionalIdeal.canonicalEquiv_selfₓ'. -/
 @[simp]
 theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ :=
   by
@@ -984,9 +1617,15 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
+/- warning: fractional_ideal.exists_ne_zero_mem_is_integer -> FractionalIdeal.exists_ne_zero_mem_isInteger is a dubious translation:
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+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {K : Type.{u1}} [_inst_4 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))] [_inst_7 : IsFractionRing.{u2, u1} R _inst_1 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6] {I : FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6} [_inst_10 : Nontrivial.{u2} R], (Ne.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6)))) -> (Exists.{succ u2} R (fun (x : R) => Exists.{0} (Ne.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (fun (H : Ne.{succ u2} R x (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => K) x) (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) R K (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) R K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))))) R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))) (RingHom.instRingHomClassRingHom.{u2, u1} R K (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))))))) (algebraMap.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4))) _inst_6) x) I)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_ne_zero_mem_is_integer FractionalIdeal.exists_ne_zero_mem_isIntegerₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 /-- Nonzero fractional ideals contain a nonzero integer. -/
-theorem exists_ne_zero_mem_is_integer [Nontrivial R] (hI : I ≠ 0) :
+theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
     ∃ (x : _)(_ : x ≠ (0 : R)), algebraMap R K x ∈ I :=
   by
   obtain ⟨y, y_mem, y_not_mem⟩ :=
@@ -998,8 +1637,14 @@ theorem exists_ne_zero_mem_is_integer [Nontrivial R] (hI : I ≠ 0) :
     exact mul_ne_zero (IsFractionRing.to_map_ne_zero_of_mem_nonZeroDivisors z.2) y_ne_zero
   · rw [hx]
     exact smul_mem _ _ y_mem
-#align fractional_ideal.exists_ne_zero_mem_is_integer FractionalIdeal.exists_ne_zero_mem_is_integer
-
+#align fractional_ideal.exists_ne_zero_mem_is_integer FractionalIdeal.exists_ne_zero_mem_isInteger
+
+/- warning: fractional_ideal.map_ne_zero -> FractionalIdeal.map_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {K : Type.{u2}} {K' : Type.{u3}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u3} K'] [_inst_6 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_4)))] [_inst_7 : IsFractionRing.{u1, u2} R _inst_1 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6] [_inst_8 : Algebra.{u1, u3} R K' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_5)))] [_inst_9 : IsFractionRing.{u1, u3} R _inst_1 K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_5)) _inst_8] {I : FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6} (h : AlgHom.{u1, u2, u3} R K K' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_4))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_5))) _inst_6 _inst_8) [_inst_10 : Nontrivial.{u1} R], (Ne.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))))) -> (Ne.{succ u3} (FractionalIdeal.{u1, u3} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_5)) _inst_8) (FractionalIdeal.map.{u1, u2, u3} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6 K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_5)) _inst_8 h I) (OfNat.ofNat.{u3} (FractionalIdeal.{u1, u3} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_5)) _inst_8) 0 (OfNat.mk.{u3} (FractionalIdeal.{u1, u3} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_5)) _inst_8) 0 (Zero.zero.{u3} (FractionalIdeal.{u1, u3} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_5)) _inst_8) (FractionalIdeal.hasZero.{u1, u3} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_5)) _inst_8)))))
+but is expected to have type
+  forall {R : Type.{u3}} [_inst_1 : CommRing.{u3} R] {K : Type.{u2}} {K' : Type.{u1}} [_inst_4 : Field.{u2} K] [_inst_5 : Field.{u1} K'] [_inst_6 : Algebra.{u3, u2} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4)))] [_inst_7 : IsFractionRing.{u3, u2} R _inst_1 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6] [_inst_8 : Algebra.{u3, u1} R K' (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_5)))] [_inst_9 : IsFractionRing.{u3, u1} R _inst_1 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_5)) _inst_8] {I : FractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6} (h : AlgHom.{u3, u2, u1} R K K' (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_4))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_5))) _inst_6 _inst_8) [_inst_10 : Nontrivial.{u3} R], (Ne.{succ u2} (FractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) I (OfNat.ofNat.{u2} (FractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u3, u2} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6)))) -> (Ne.{succ u1} (FractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_5)) _inst_8) (FractionalIdeal.map.{u3, u2, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_5)) _inst_8 h I) (OfNat.ofNat.{u1} (FractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_5)) _inst_8) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_5)) _inst_8) (FractionalIdeal.instZeroFractionalIdeal.{u3, u1} R _inst_1 (nonZeroDivisors.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_5)) _inst_8))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_ne_zero FractionalIdeal.map_ne_zeroₓ'. -/
 theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 :=
   by
   obtain ⟨x, x_ne_zero, hx⟩ := exists_ne_zero_mem_is_integer hI
@@ -1008,37 +1653,79 @@ theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 :=
   exact ⟨algebraMap R K x, hx, h.commutes x⟩
 #align fractional_ideal.map_ne_zero FractionalIdeal.map_ne_zero
 
+/- warning: fractional_ideal.map_eq_zero_iff -> FractionalIdeal.map_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_eq_zero_iff FractionalIdeal.map_eq_zero_iffₓ'. -/
 @[simp]
 theorem map_eq_zero_iff [Nontrivial R] : I.map h = 0 ↔ I = 0 :=
   ⟨imp_of_not_imp_not _ _ (map_ne_zero _), fun hI => hI.symm ▸ map_zero h⟩
 #align fractional_ideal.map_eq_zero_iff FractionalIdeal.map_eq_zero_iff
 
-theorem coe_ideal_injective : Function.Injective (coe : Ideal R → FractionalIdeal R⁰ K) :=
-  coe_ideal_injective' le_rfl
-#align fractional_ideal.coe_ideal_injective FractionalIdeal.coe_ideal_injective
-
-theorem coe_ideal_inj {I J : Ideal R} :
+/- warning: fractional_ideal.coe_ideal_injective -> FractionalIdeal.coeIdeal_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {K : Type.{u2}} [_inst_4 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_4)))] [_inst_7 : IsFractionRing.{u1, u2} R _inst_1 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6], Function.Injective.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {K : Type.{u1}} [_inst_4 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))] [_inst_7 : IsFractionRing.{u2, u1} R _inst_1 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6], Function.Injective.{succ u2, succ u1} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) (fun (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_injective FractionalIdeal.coeIdeal_injectiveₓ'. -/
+theorem coeIdeal_injective : Function.Injective (coe : Ideal R → FractionalIdeal R⁰ K) :=
+  coeIdeal_injective' le_rfl
+#align fractional_ideal.coe_ideal_injective FractionalIdeal.coeIdeal_injective
+
+/- warning: fractional_ideal.coe_ideal_inj -> FractionalIdeal.coeIdeal_inj is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {K : Type.{u2}} [_inst_4 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_4)))] [_inst_7 : IsFractionRing.{u1, u2} R _inst_1 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {J : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))) I) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))) J)) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I J)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {K : Type.{u1}} [_inst_4 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))] [_inst_7 : IsFractionRing.{u2, u1} R _inst_1 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))} {J : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, Iff (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6 I) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6 J)) (Eq.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) I J)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_inj FractionalIdeal.coeIdeal_injₓ'. -/
+theorem coeIdeal_inj {I J : Ideal R} :
     (I : FractionalIdeal R⁰ K) = (J : FractionalIdeal R⁰ K) ↔ I = J :=
-  coe_ideal_inj' le_rfl
-#align fractional_ideal.coe_ideal_inj FractionalIdeal.coe_ideal_inj
-
+  coeIdeal_inj' le_rfl
+#align fractional_ideal.coe_ideal_inj FractionalIdeal.coeIdeal_inj
+
+/- warning: fractional_ideal.coe_ideal_eq_zero -> FractionalIdeal.coeIdeal_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {K : Type.{u2}} [_inst_4 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_4)))] [_inst_7 : IsFractionRing.{u1, u2} R _inst_1 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))) I) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))))) (Eq.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_eq_zero FractionalIdeal.coeIdeal_eq_zeroₓ'. -/
 @[simp]
-theorem coe_ideal_eq_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 0 ↔ I = ⊥ :=
-  coe_ideal_eq_zero' le_rfl
-#align fractional_ideal.coe_ideal_eq_zero FractionalIdeal.coe_ideal_eq_zero
-
-theorem coe_ideal_ne_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 0 ↔ I ≠ ⊥ :=
-  coe_ideal_ne_zero' le_rfl
-#align fractional_ideal.coe_ideal_ne_zero FractionalIdeal.coe_ideal_ne_zero
-
+theorem coeIdeal_eq_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 0 ↔ I = ⊥ :=
+  coeIdeal_eq_zero' le_rfl
+#align fractional_ideal.coe_ideal_eq_zero FractionalIdeal.coeIdeal_eq_zero
+
+/- warning: fractional_ideal.coe_ideal_ne_zero -> FractionalIdeal.coeIdeal_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {K : Type.{u2}} [_inst_4 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_4)))] [_inst_7 : IsFractionRing.{u1, u2} R _inst_1 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Ne.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))) I) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))))) (Ne.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (Bot.bot.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.hasBot.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_ne_zero FractionalIdeal.coeIdeal_ne_zeroₓ'. -/
+theorem coeIdeal_ne_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 0 ↔ I ≠ ⊥ :=
+  coeIdeal_ne_zero' le_rfl
+#align fractional_ideal.coe_ideal_ne_zero FractionalIdeal.coeIdeal_ne_zero
+
+/- warning: fractional_ideal.coe_ideal_eq_one -> FractionalIdeal.coeIdeal_eq_one is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_eq_one FractionalIdeal.coeIdeal_eq_oneₓ'. -/
 @[simp]
-theorem coe_ideal_eq_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 1 ↔ I = 1 := by
+theorem coeIdeal_eq_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 1 ↔ I = 1 := by
   simpa only [Ideal.one_eq_top] using coe_ideal_inj
-#align fractional_ideal.coe_ideal_eq_one FractionalIdeal.coe_ideal_eq_one
-
-theorem coe_ideal_ne_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 1 ↔ I ≠ 1 :=
-  not_iff_not.mpr coe_ideal_eq_one
-#align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coe_ideal_ne_one
+#align fractional_ideal.coe_ideal_eq_one FractionalIdeal.coeIdeal_eq_one
+
+/- warning: fractional_ideal.coe_ideal_ne_one -> FractionalIdeal.coeIdeal_ne_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {K : Type.{u2}} [_inst_4 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_4)))] [_inst_7 : IsFractionRing.{u1, u2} R _inst_1 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Ne.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))) I) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R _inst_1 (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_4)) _inst_6))))) (Ne.{succ u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) I (OfNat.ofNat.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (OfNat.mk.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 1 (One.one.{u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.one.{u1, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {K : Type.{u1}} [_inst_4 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R K (CommRing.toCommSemiring.{u2} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_4)))] [_inst_7 : IsFractionRing.{u2, u1} R _inst_1 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6] {I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, Iff (Ne.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) (FractionalIdeal.coeIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6 I) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R _inst_1 (nonZeroDivisors.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_4)) _inst_6)))) (Ne.{succ u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) I (OfNat.ofNat.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) 1 (One.toOfNat1.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Submodule.one.{u2, u2} R (CommRing.toCommSemiring.{u2} R _inst_1) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coeIdeal_ne_oneₓ'. -/
+theorem coeIdeal_ne_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 1 ↔ I ≠ 1 :=
+  not_iff_not.mpr coeIdeal_eq_one
+#align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coeIdeal_ne_one
 
 end IsFractionRing
 
@@ -1070,6 +1757,12 @@ instance : Nontrivial (FractionalIdeal R₁⁰ K) :=
         simpa only [h] using coe_mem_one R₁⁰ 1
       one_ne_zero ((mem_zero_iff _).mp this)⟩⟩
 
+/- warning: fractional_ideal.ne_zero_of_mul_eq_one -> FractionalIdeal.ne_zero_of_mul_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6), (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I J) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] (I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6), (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) I J) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.ne_zero_of_mul_eq_one FractionalIdeal.ne_zero_of_mul_eq_oneₓ'. -/
 theorem ne_zero_of_mul_eq_one (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : I ≠ 0 := fun hI =>
   zero_ne_one' (FractionalIdeal R₁⁰ K)
     (by
@@ -1081,6 +1774,12 @@ variable [IsDomain R₁]
 
 include frac
 
+/- warning: is_fractional.div_of_nonzero -> IsFractional.div_of_nonzero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)} {J : Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)}, (IsFractional.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 I) -> (IsFractional.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 J) -> (Ne.{succ u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) J (OfNat.ofNat.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) 0 (OfNat.mk.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) 0 (Zero.zero.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (MulZeroClass.toHasZero.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.idemSemiring.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)))))))))) -> (IsFractional.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (instHDiv.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.hasDiv.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) _inst_6)) I J))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)} {J : Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)}, (IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) -> (IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J) -> (Ne.{succ u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) J (OfNat.ofNat.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) 0 (Zero.toOfNat0.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (CommMonoidWithZero.toZero.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (CommSemiring.toCommMonoidWithZero.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (IdemCommSemiring.toCommSemiring.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6))))))) -> (IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (instHDiv.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6)) I J))
+Case conversion may be inaccurate. Consider using '#align is_fractional.div_of_nonzero IsFractional.div_of_nonzeroₓ'. -/
 theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     IsFractional R₁⁰ I → IsFractional R₁⁰ J → J ≠ 0 → IsFractional R₁⁰ (I / J)
   | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩, h =>
@@ -1105,10 +1804,16 @@ theorem IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
     rw [← hy', mul_comm b, ← Algebra.smul_def, mul_smul]
 #align is_fractional.div_of_nonzero IsFractional.div_of_nonzero
 
+/- warning: fractional_ideal.fractional_div_of_nonzero -> FractionalIdeal.fractional_div_of_nonzero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (IsFractional.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (instHDiv.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.hasDiv.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) J)))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} 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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.fractional_div_of_nonzero FractionalIdeal.fractional_div_of_nonzeroₓ'. -/
 theorem fractional_div_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     IsFractional R₁⁰ (I / J : Submodule R₁ K) :=
   I.IsFractional.div_of_nonzero J.IsFractional fun H =>
-    h <| coe_to_submodule_injective <| H.trans coe_zero.symm
+    h <| coeToSubmodule_injective <| H.trans coe_zero.symm
 #align fractional_ideal.fractional_div_of_nonzero FractionalIdeal.fractional_div_of_nonzero
 
 noncomputable instance : Div (FractionalIdeal R₁⁰ K) :=
@@ -1116,28 +1821,58 @@ noncomputable instance : Div (FractionalIdeal R₁⁰ K) :=
 
 variable {I J : FractionalIdeal R₁⁰ K} [J ≠ 0]
 
+/- warning: fractional_ideal.div_zero -> FractionalIdeal.div_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_zero FractionalIdeal.div_zeroₓ'. -/
 @[simp]
 theorem div_zero {I : FractionalIdeal R₁⁰ K} : I / 0 = 0 :=
   dif_pos rfl
 #align fractional_ideal.div_zero FractionalIdeal.div_zero
 
+/- warning: fractional_ideal.div_nonzero -> FractionalIdeal.div_nonzero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} (h : Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))), Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J) (Subtype.mk.{succ u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (fun (I : Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) => IsFractional.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 I) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (instHDiv.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (Submodule.hasDiv.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5))))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) J)) (FractionalIdeal.fractional_div_of_nonzero.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7 I J h))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} (h : Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) J (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))), Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J) (Subtype.mk.{succ u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (fun (I : Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) => IsFractional.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (instHDiv.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6)) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J)) (FractionalIdeal.fractional_div_of_nonzero.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7 I J h))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_nonzero FractionalIdeal.div_nonzeroₓ'. -/
 theorem div_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
     I / J = ⟨I / J, fractional_div_of_nonzero h⟩ :=
   dif_neg h
 #align fractional_ideal.div_nonzero FractionalIdeal.div_nonzero
 
+/- warning: fractional_ideal.coe_div -> FractionalIdeal.coe_div is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (Eq.{succ u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) 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(Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J)) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (instHDiv.{u2} (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (Submodule.hasDiv.{u1, u2} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Submodule.{u1, u2} R₁ K (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} K (NonUnitalNonAssocRing.toAddCommGroup.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))) (Algebra.toModule.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) J)))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, (Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) J (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (Eq.{succ u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J)) (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (instHDiv.{u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) _inst_6)) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_div FractionalIdeal.coe_divₓ'. -/
 @[simp]
 theorem coe_div {I J : FractionalIdeal R₁⁰ K} (hJ : J ≠ 0) :
     (↑(I / J) : Submodule R₁ K) = ↑I / (↑J : Submodule R₁ K) :=
   congr_arg _ (dif_neg hJ)
 #align fractional_ideal.coe_div FractionalIdeal.coe_div
 
+/- warning: fractional_ideal.mem_div_iff_of_nonzero -> FractionalIdeal.mem_div_iff_of_nonzero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (forall {x : K}, Iff (Membership.Mem.{u2, u2} K (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) x (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J)) (forall (y : K), (Membership.Mem.{u2, u2} K (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) y J) -> (Membership.Mem.{u2, u2} K (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) x y) I)))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} 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(Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (forall {x : K}, Iff (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) x (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J)) (forall (y : K), (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) y J) -> (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) x y) I)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzeroₓ'. -/
 theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {x} :
     x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I := by
   rw [div_nonzero h]
   exact Submodule.mem_div_iff_forall_mul_mem
 #align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzero
 
+/- warning: fractional_ideal.mul_one_div_le_one -> FractionalIdeal.mul_one_div_le_one is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, LE.le.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 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_inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I)) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K 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R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))) I)) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_oneₓ'. -/
 theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :=
   by
   by_cases hI : I = 0
@@ -1147,6 +1882,12 @@ theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :
     apply Submodule.mul_one_div_le_one
 #align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_one
 
+/- warning: fractional_ideal.le_self_mul_one_div -> FractionalIdeal.le_self_mul_one_div is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (LE.le.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (LE.le.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.partialOrder.{u2, u2} 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K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I)))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, (LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Lattice.toSemilatticeInf.{u1} 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(CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.lattice.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))) I (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) I (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))) I)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_divₓ'. -/
 theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
     I ≤ I * (1 / I) := by
   by_cases hI_nz : I = 0
@@ -1157,12 +1898,24 @@ theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : Fra
     exact Submodule.le_self_mul_one_div hI
 #align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_div
 
+/- warning: fractional_ideal.le_div_iff_of_nonzero -> FractionalIdeal.le_div_iff_of_nonzero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J' : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J' (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ 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_inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) J J')) (forall (x : K), (Membership.Mem.{u2, u2} K (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) x I) -> (forall (y : K), (Membership.Mem.{u2, u2} K (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) y J') -> (Membership.Mem.{u2, u2} K (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) x y) J))))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J' : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, (Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) J' (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.lattice.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))) I (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) J J')) (forall (x : K), (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) x I) -> (forall (y : K), (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) y J') -> (Membership.mem.{u1, u1} K (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) K (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5)))))) x y) J))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzeroₓ'. -/
 theorem le_div_iff_of_nonzero {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ ∀ x ∈ I, ∀ y ∈ J', x * y ∈ J :=
   ⟨fun h x hx => (mem_div_iff_of_nonzero hJ').mp (h hx), fun h x hx =>
     (mem_div_iff_of_nonzero hJ').mpr (h x hx)⟩
 #align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzero
 
+/- warning: fractional_ideal.le_div_iff_mul_le -> FractionalIdeal.le_div_iff_mul_le is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6} {J' : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J' (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 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(nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I J') J))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6} {J' : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, (Ne.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) J' (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.lattice.{u2, u1} R₁ _inst_4 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(Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) J J')) (LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K 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(FractionalIdeal.lattice.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) I J') J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_div_iff_mul_le FractionalIdeal.le_div_iff_mul_leₓ'. -/
 theorem le_div_iff_mul_le {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
     I ≤ J / J' ↔ I * J' ≤ J := by
   rw [div_nonzero hJ']
@@ -1170,6 +1923,12 @@ theorem le_div_iff_mul_le {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0)
   rw [← coe_mul, coe_le_coe]
 #align fractional_ideal.le_div_iff_mul_le FractionalIdeal.le_div_iff_mul_le
 
+/- warning: fractional_ideal.div_one -> FractionalIdeal.div_one is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) I
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) I
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_one FractionalIdeal.div_oneₓ'. -/
 @[simp]
 theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I :=
   by
@@ -1184,6 +1943,12 @@ theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I :=
     exact (Algebra.smul_def _ _).symm
 #align fractional_ideal.div_one FractionalIdeal.div_one
 
+/- warning: fractional_ideal.eq_one_div_of_mul_eq_one_right -> FractionalIdeal.eq_one_div_of_mul_eq_one_right is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6), (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I J) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) -> (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) J (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ 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(FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] (I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6), (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) I J) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) -> (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) J (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ 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(FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))) I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_rightₓ'. -/
 theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : J = 1 / I :=
   by
   have hI : I ≠ 0 := ne_zero_of_mul_eq_one I J h
@@ -1205,12 +1970,24 @@ theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I
   exact mul_mem_mul hx hy
 #align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_right
 
+/- warning: fractional_ideal.mul_div_self_cancel_iff -> FractionalIdeal.mul_div_self_cancel_iff is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) I)) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) (Exists.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (fun (J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) => Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I J) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, Iff (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) I (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))) I)) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))) (Exists.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (fun (J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) => Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) I J) (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iffₓ'. -/
 theorem mul_div_self_cancel_iff {I : FractionalIdeal R₁⁰ K} : I * (1 / I) = 1 ↔ ∃ J, I * J = 1 :=
   ⟨fun h => ⟨1 / I, h⟩, fun ⟨J, hJ⟩ => by rwa [← eq_one_div_of_mul_eq_one_right I J hJ]⟩
 #align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iff
 
 variable {K' : Type _} [Field K'] [Algebra R₁ K'] [IsFractionRing R₁ K']
 
+/- warning: fractional_ideal.map_div -> FractionalIdeal.map_div is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {K' : Type.{u3}} [_inst_9 : Field.{u3} K'] [_inst_10 : Algebra.{u1, u3} R₁ K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9)))] [_inst_11 : IsFractionRing.{u1, u3} R₁ _inst_4 K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)) _inst_10] (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ 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K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u3, u1, u2, u3} (AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (Ring.toSemiring.{u3} K' (CommRing.toRing.{u3} K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.algEquivClass.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10))))) h) J))
+but is expected to have type
+  forall {R₁ : Type.{u3}} [_inst_4 : CommRing.{u3} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u3, u2} R₁ K (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))] [frac : IsFractionRing.{u3, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4))] {K' : Type.{u1}} [_inst_9 : Field.{u1} K'] [_inst_10 : Algebra.{u3, u1} R₁ K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9)))] [_inst_11 : IsFractionRing.{u3, u1} R₁ _inst_4 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10] (I : FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (J : FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (h : AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10), Eq.{succ u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.map.{u3, u2, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10 (AlgHomClass.toAlgHom.{u3, u2, u1, max u2 u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10 (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10)) h) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u3, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) I J)) (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (instHDiv.{u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u3, u1} R₁ _inst_4 K' _inst_9 _inst_10 _inst_11 _inst_7)) (FractionalIdeal.map.{u3, u2, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10 (AlgHomClass.toAlgHom.{u3, u2, u1, max u2 u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (CommSemiring.toSemiring.{u1} K' (CommRing.toCommSemiring.{u1} K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (CommSemiring.toSemiring.{u1} K' (CommRing.toCommSemiring.{u1} K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10)) h) I) (FractionalIdeal.map.{u3, u2, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10 (AlgHomClass.toAlgHom.{u3, u2, u1, max u2 u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (CommSemiring.toSemiring.{u1} K' (CommRing.toCommSemiring.{u1} K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (CommSemiring.toSemiring.{u1} K' (CommRing.toCommSemiring.{u1} K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10)) h) J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_div FractionalIdeal.map_divₓ'. -/
 @[simp]
 theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     (I / J).map (h : K →ₐ[R₁] K') = I.map h / J.map h :=
@@ -1221,6 +1998,12 @@ theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     simp [div_nonzero H, div_nonzero (map_ne_zero _ H), Submodule.map_div]
 #align fractional_ideal.map_div FractionalIdeal.map_div
 
+/- warning: fractional_ideal.map_one_div -> FractionalIdeal.map_one_div is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] {K' : Type.{u3}} [_inst_9 : Field.{u3} K'] [_inst_10 : Algebra.{u1, u3} R₁ K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9)))] [_inst_11 : IsFractionRing.{u1, u3} R₁ _inst_4 K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)) _inst_10] (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (h : AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10), Eq.{succ u3} (FractionalIdeal.{u1, u3} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)) _inst_10) (FractionalIdeal.map.{u1, u2, u3} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)) _inst_10 ((fun (a : Sort.{max (succ u2) (succ u3)}) (b : Sort.{max (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3), max (succ u2) (succ u3)} a b] => self.0) (AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) (AlgHom.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) (HasLiftT.mk.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' 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(Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)) _inst_10 ((fun (a : Sort.{max (succ u2) (succ u3)}) (b : Sort.{max (succ u2) (succ u3)}) [self : HasLiftT.{max (succ u2) (succ u3), max (succ u2) (succ u3)} a b] => self.0) (AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) (AlgHom.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (Ring.toSemiring.{u3} K' (CommRing.toRing.{u3} K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)))) _inst_6 _inst_10) (HasLiftT.mk.{max (succ u2) (succ u3), max (succ u2) (succ u3)} 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(CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (Ring.toSemiring.{u3} K' (CommRing.toRing.{u3} K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)))) _inst_6 _inst_10) (AlgHomClass.coeTC.{u1, u2, u3, max u2 u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (Ring.toSemiring.{u3} K' (CommRing.toRing.{u3} K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u3, u1, u2, u3} (AlgEquiv.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (CommRing.toRing.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (Ring.toSemiring.{u3} K' (CommRing.toRing.{u3} K' (EuclideanDomain.toCommRing.{u3} K' (Field.toEuclideanDomain.{u3} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.algEquivClass.{u1, u2, u3} R₁ K K' (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (Ring.toSemiring.{u3} K' (DivisionRing.toRing.{u3} K' (Field.toDivisionRing.{u3} K' _inst_9))) _inst_6 _inst_10))))) h) I))
+but is expected to have type
+  forall {R₁ : Type.{u3}} [_inst_4 : CommRing.{u3} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u3, u2} R₁ K (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))] [frac : IsFractionRing.{u3, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4))] {K' : Type.{u1}} [_inst_9 : Field.{u1} K'] [_inst_10 : Algebra.{u3, u1} R₁ K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9)))] [_inst_11 : IsFractionRing.{u3, u1} R₁ _inst_4 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10] (I : FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (h : AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10), Eq.{succ u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.map.{u3, u2, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10 (AlgHomClass.toAlgHom.{u3, u2, u1, max u2 u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10 (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10)) h) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u3, u2} R₁ _inst_4 K _inst_5 _inst_6 frac _inst_7)) (OfNat.ofNat.{u2} (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u2} (FractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u3, u2} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))) I)) (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (instHDiv.{u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u3, u1} R₁ _inst_4 K' _inst_9 _inst_10 _inst_11 _inst_7)) (OfNat.ofNat.{u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10) (FractionalIdeal.instOneFractionalIdeal.{u3, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10))) (FractionalIdeal.map.{u3, u2, u1} R₁ _inst_4 (nonZeroDivisors.{u3} R₁ (Semiring.toMonoidWithZero.{u3} R₁ (CommSemiring.toSemiring.{u3} R₁ (CommRing.toCommSemiring.{u3} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)) _inst_10 (AlgHomClass.toAlgHom.{u3, u2, u1, max u2 u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (CommSemiring.toSemiring.{u1} K' (CommRing.toCommSemiring.{u1} K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) (AlgEquivClass.toAlgHomClass.{max u2 u1, u3, u2, u1} (AlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10) R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (CommSemiring.toSemiring.{u2} K (CommRing.toCommSemiring.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)))) (CommSemiring.toSemiring.{u1} K' (CommRing.toCommSemiring.{u1} K' (EuclideanDomain.toCommRing.{u1} K' (Field.toEuclideanDomain.{u1} K' _inst_9)))) _inst_6 _inst_10 (AlgEquiv.instAlgEquivClassAlgEquiv.{u3, u2, u1} R₁ K K' (CommRing.toCommSemiring.{u3} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))) (DivisionSemiring.toSemiring.{u1} K' (Semifield.toDivisionSemiring.{u1} K' (Field.toSemifield.{u1} K' _inst_9))) _inst_6 _inst_10)) h) I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.map_one_div FractionalIdeal.map_one_divₓ'. -/
 @[simp]
 theorem map_one_div (I : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
     (1 / I).map (h : K →ₐ[R₁] K') = 1 / I.map h := by rw [map_div, map_one]
@@ -1234,6 +2017,12 @@ variable {R₁ K L : Type _} [CommRing R₁] [Field K] [Field L]
 
 variable [Algebra R₁ K] [IsFractionRing R₁ K] [Algebra K L] [IsFractionRing K L]
 
+/- warning: fractional_ideal.eq_zero_or_one -> FractionalIdeal.eq_zero_or_one is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {L : Type.{u2}} [_inst_5 : Field.{u1} K] [_inst_6 : Field.{u2} L] [_inst_9 : Algebra.{u1, u2} K L (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)) (Ring.toSemiring.{u2} L (DivisionRing.toRing.{u2} L (Field.toDivisionRing.{u2} L _inst_6)))] [_inst_10 : IsFractionRing.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9] (I : FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9), Or (Eq.{succ u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) (FractionalIdeal.hasZero.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9))))) (Eq.{succ u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9) (FractionalIdeal.hasOne.{u1, u2} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) (nonZeroDivisors.{u1} K (Semiring.toMonoidWithZero.{u1} K (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_5))))) L (EuclideanDomain.toCommRing.{u2} L (Field.toEuclideanDomain.{u2} L _inst_6)) _inst_9)))))
+but is expected to have type
+  forall {K : Type.{u2}} {L : Type.{u1}} [_inst_5 : Field.{u2} K] [_inst_6 : Field.{u1} L] [_inst_9 : Algebra.{u2, u1} K L (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)) (DivisionSemiring.toSemiring.{u1} L (Semifield.toDivisionSemiring.{u1} L (Field.toSemifield.{u1} L _inst_6)))] [_inst_10 : IsFractionRing.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9] (I : FractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9), Or (Eq.{succ u1} (FractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9)))) (Eq.{succ u1} (FractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) (nonZeroDivisors.{u2} K (Semiring.toMonoidWithZero.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5))))) L (EuclideanDomain.toCommRing.{u1} L (Field.toEuclideanDomain.{u1} L _inst_6)) _inst_9))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_oneₓ'. -/
 theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
   by
   rw [or_iff_not_imp_left]
@@ -1251,6 +2040,12 @@ theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 :=
     exact Submodule.smul_mem I _ y_mem
 #align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_one
 
+/- warning: fractional_ideal.eq_zero_or_one_of_is_field -> FractionalIdeal.eq_zero_or_one_of_isField is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} {K : Type.{u2}} [_inst_4 : CommRing.{u1} R₁] [_inst_5 : Field.{u2} K] [_inst_7 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_8 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7], (IsField.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) -> (forall (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7), Or (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7))))) (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) I (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_7))))))
+but is expected to have type
+  forall {R₁ : Type.{u2}} {K : Type.{u1}} [_inst_4 : CommRing.{u2} R₁] [_inst_5 : Field.{u1} K] [_inst_7 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [_inst_8 : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7], (IsField.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) -> (forall (I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7), Or (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7)))) (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7) I (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7) 1 (One.toOfNat1.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7) (FractionalIdeal.instOneFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_7)))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_zero_or_one_of_is_field FractionalIdeal.eq_zero_or_one_of_isFieldₓ'. -/
 theorem eq_zero_or_one_of_isField (hF : IsField R₁) (I : FractionalIdeal R₁⁰ K) : I = 0 ∨ I = 1 :=
   letI : Field R₁ := hF.to_field
   eq_zero_or_one I
@@ -1268,6 +2063,7 @@ open Classical
 
 variable (R₁)
 
+#print FractionalIdeal.spanFinset /-
 /-- `fractional_ideal.span_finset R₁ s f` is the fractional ideal of `R₁` generated by `f '' s`. -/
 @[simps]
 def spanFinset {ι : Type _} (s : Finset ι) (f : ι → K) : FractionalIdeal R₁⁰ K :=
@@ -1286,9 +2082,16 @@ def spanFinset {ι : Type _} (s : Finset ι) (f : ι → K) : FractionalIdeal R
       rw [smul_comm]
       exact IsLocalization.isInteger_smul hx⟩
 #align fractional_ideal.span_finset FractionalIdeal.spanFinset
+-/
 
 variable {R₁}
 
+/- warning: fractional_ideal.span_finset_eq_zero -> FractionalIdeal.spanFinset_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> K}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.spanFinset.{u1, u2, u3} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 ι s f) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) (forall (j : ι), (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) j s) -> (Eq.{succ u2} K (f j) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))))))))))
+but is expected to have type
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> K}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.spanFinset.{u1, u2, u3} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 ι s f) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) (forall (j : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) j s) -> (Eq.{succ u2} K (f j) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5))))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_finset_eq_zero FractionalIdeal.spanFinset_eq_zeroₓ'. -/
 @[simp]
 theorem spanFinset_eq_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f = 0 ↔ ∀ j ∈ s, f j = 0 := by
@@ -1296,6 +2099,12 @@ theorem spanFinset_eq_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     Set.mem_image, Finset.mem_coe, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
 #align fractional_ideal.span_finset_eq_zero FractionalIdeal.spanFinset_eq_zero
 
+/- warning: fractional_ideal.span_finset_ne_zero -> FractionalIdeal.spanFinset_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> K}, Iff (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.spanFinset.{u1, u2, u3} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 ι s f) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) (Exists.{succ u3} ι (fun (j : ι) => Exists.{0} (Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) j s) (fun (H : Membership.Mem.{u3, u3} ι (Finset.{u3} ι) (Finset.hasMem.{u3} ι) j s) => Ne.{succ u2} K (f j) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))))))))))))
+but is expected to have type
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] {ι : Type.{u3}} {s : Finset.{u3} ι} {f : ι -> K}, Iff (Ne.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.spanFinset.{u1, u2, u3} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 ι s f) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) (Exists.{succ u3} ι (fun (j : ι) => And (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) j s) (Ne.{succ u2} K (f j) (OfNat.ofNat.{u2} K 0 (Zero.toOfNat0.{u2} K (CommMonoidWithZero.toZero.{u2} K (CommGroupWithZero.toCommMonoidWithZero.{u2} K (Semifield.toCommGroupWithZero.{u2} K (Field.toSemifield.{u2} K _inst_5)))))))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_finset_ne_zero FractionalIdeal.spanFinset_ne_zeroₓ'. -/
 theorem spanFinset_ne_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f ≠ 0 ↔ ∃ j ∈ s, f j ≠ 0 := by simp
 #align fractional_ideal.span_finset_ne_zero FractionalIdeal.spanFinset_ne_zero
@@ -1304,6 +2113,12 @@ open Submodule.IsPrincipal
 
 include loc
 
+/- warning: fractional_ideal.is_fractional_span_singleton -> FractionalIdeal.isFractional_span_singleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (x : P), IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Submodule.span.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.hasSingleton.{u2} P) x))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] (x : P), IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (Submodule.span.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) x))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_span_singleton FractionalIdeal.isFractional_span_singletonₓ'. -/
 theorem isFractional_span_singleton (x : P) : IsFractional S (span R {x} : Submodule R P) :=
   let ⟨a, ha⟩ := exists_integer_multiple S x
   isFractional_span_iff.mpr ⟨a, a.2, fun x' hx' => (Set.mem_singleton_iff.mp hx').symm ▸ ha⟩
@@ -1311,11 +2126,14 @@ theorem isFractional_span_singleton (x : P) : IsFractional S (span R {x} : Submo
 
 variable (S)
 
+#print FractionalIdeal.spanSingleton /-
 /-- `span_singleton x` is the fractional ideal generated by `x` if `0 ∉ S` -/
 irreducible_def spanSingleton (x : P) : FractionalIdeal S P :=
   ⟨span R {x}, isFractional_span_singleton x⟩
 #align fractional_ideal.span_singleton FractionalIdeal.spanSingleton
+-/
 
+#print FractionalIdeal.coe_spanSingleton /-
 -- local attribute [semireducible] span_singleton
 @[simp]
 theorem coe_spanSingleton (x : P) : (spanSingleton S x : Submodule R P) = span R {x} :=
@@ -1323,26 +2141,43 @@ theorem coe_spanSingleton (x : P) : (spanSingleton S x : Submodule R P) = span R
   rw [span_singleton]
   rfl
 #align fractional_ideal.coe_span_singleton FractionalIdeal.coe_spanSingleton
+-/
 
+#print FractionalIdeal.mem_spanSingleton /-
 @[simp]
 theorem mem_spanSingleton {x y : P} : x ∈ spanSingleton S y ↔ ∃ z : R, z • y = x :=
   by
   rw [span_singleton]
   exact Submodule.mem_span_singleton
 #align fractional_ideal.mem_span_singleton FractionalIdeal.mem_spanSingleton
+-/
 
+#print FractionalIdeal.mem_spanSingleton_self /-
 theorem mem_spanSingleton_self (x : P) : x ∈ spanSingleton S x :=
   (mem_spanSingleton S).mpr ⟨1, one_smul _ _⟩
 #align fractional_ideal.mem_span_singleton_self FractionalIdeal.mem_spanSingleton_self
+-/
 
 variable {S}
 
+/- warning: fractional_ideal.span_singleton_le_iff_mem -> FractionalIdeal.spanSingleton_le_iff_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc x) I) (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) x I)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc x) I) (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) x I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_le_iff_mem FractionalIdeal.spanSingleton_le_iff_memₓ'. -/
 @[simp]
 theorem spanSingleton_le_iff_mem {x : P} {I : FractionalIdeal S P} :
     spanSingleton S x ≤ I ↔ x ∈ I := by
   rw [← coe_le_coe, coe_span_singleton, Submodule.span_singleton_le_iff_mem x ↑I, mem_coe]
 #align fractional_ideal.span_singleton_le_iff_mem FractionalIdeal.spanSingleton_le_iff_mem
 
+/- warning: fractional_ideal.span_singleton_eq_span_singleton -> FractionalIdeal.spanSingleton_eq_spanSingleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] [_inst_8 : NoZeroSMulDivisors.{u1, u2} R P (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} P (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} P (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R P (AddZeroClass.toHasZero.{u2} P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R P (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))))] {x : P} {y : P}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc x) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc y)) (Exists.{succ u1} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) (fun (z : Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) => Eq.{succ u2} P (SMul.smul.{u1, u2} (Units.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1))) P (Units.hasSmul.{u1, u2} R P (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)) (SMulZeroClass.toHasSmul.{u1, u2} R P (AddZeroClass.toHasZero.{u2} P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R P (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R P (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} P (AddMonoid.toAddZeroClass.{u2} P (AddCommMonoid.toAddMonoid.{u2} P (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))))) z x) y))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] [_inst_8 : NoZeroSMulDivisors.{u2, u1} R P (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} P (CommSemiring.toCommMonoidWithZero.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))) (Algebra.toSMul.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)] {x : P} {y : P}, Iff (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc x) (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc y)) (Exists.{succ u2} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (z : Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => Eq.{succ u1} P (HSMul.hSMul.{u2, u1, u1} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) P P (instHSMul.{u2, u1} (Units.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) P (Units.instSMulUnits.{u2, u1} R P (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (Algebra.toSMul.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3))) z x) y))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_eq_span_singleton FractionalIdeal.spanSingleton_eq_spanSingletonₓ'. -/
 theorem spanSingleton_eq_spanSingleton [NoZeroSMulDivisors R P] {x y : P} :
     spanSingleton S x = spanSingleton S y ↔ ∃ z : Rˣ, z • x = y :=
   by
@@ -1350,6 +2185,12 @@ theorem spanSingleton_eq_spanSingleton [NoZeroSMulDivisors R P] {x y : P} :
   exact Subtype.mk_eq_mk
 #align fractional_ideal.span_singleton_eq_span_singleton FractionalIdeal.spanSingleton_eq_spanSingleton
 
+/- warning: fractional_ideal.eq_span_singleton_of_principal -> FractionalIdeal.eq_spanSingleton_of_principal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) [_inst_8 : Submodule.IsPrincipal.{u1, u2} R P (CommRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) 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(Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I)], Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc (Submodule.IsPrincipal.generator.{u1, u2} R P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (CommRing.toRing.{u1} R _inst_1) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I) _inst_8))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) [_inst_8 : Submodule.IsPrincipal.{u2, u1} R P (CommRing.toRing.{u2} R _inst_1) (Ring.toAddCommGroup.{u1} P (CommRing.toRing.{u1} P _inst_2)) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)], Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc (Submodule.IsPrincipal.generator.{u2, u1} R P (Ring.toAddCommGroup.{u1} P (CommRing.toRing.{u1} P _inst_2)) (CommRing.toRing.{u2} R _inst_1) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I) _inst_8))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_span_singleton_of_principal FractionalIdeal.eq_spanSingleton_of_principalₓ'. -/
 theorem eq_spanSingleton_of_principal (I : FractionalIdeal S P) [IsPrincipal (I : Submodule R P)] :
     I = spanSingleton S (generator (I : Submodule R P)) :=
   by
@@ -1357,12 +2198,24 @@ theorem eq_spanSingleton_of_principal (I : FractionalIdeal S P) [IsPrincipal (I
   exact coe_to_submodule_injective (span_singleton_generator ↑I).symm
 #align fractional_ideal.eq_span_singleton_of_principal FractionalIdeal.eq_spanSingleton_of_principal
 
+/- warning: fractional_ideal.is_principal_iff -> FractionalIdeal.isPrincipal_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3), Iff (Submodule.IsPrincipal.{u1, u2} R P (CommRing.toRing.{u1} R _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2)))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (coeBase.{succ u2, succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Submodule.{u1, u2} R P (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} P (NonUnitalNonAssocRing.toAddCommGroup.{u2} P (NonAssocRing.toNonUnitalNonAssocRing.{u2} P (Ring.toNonAssocRing.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I)) (Exists.{succ u2} P (fun (x : P) => Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc x)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] (I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3), Iff (Submodule.IsPrincipal.{u2, u1} R P (CommRing.toRing.{u2} R _inst_1) (Ring.toAddCommGroup.{u1} P (CommRing.toRing.{u1} P _inst_2)) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (FractionalIdeal.coeToSubmodule.{u2, u1} R _inst_1 S P _inst_2 _inst_3 I)) (Exists.{succ u1} P (fun (x : P) => Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc x)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_principal_iff FractionalIdeal.isPrincipal_iffₓ'. -/
 theorem isPrincipal_iff (I : FractionalIdeal S P) :
     IsPrincipal (I : Submodule R P) ↔ ∃ x, I = spanSingleton S x :=
   ⟨fun h => ⟨@generator _ _ _ _ _ (↑I) h, @eq_spanSingleton_of_principal _ _ _ _ _ _ _ I h⟩,
     fun ⟨x, hx⟩ => { principal := ⟨x, trans (congr_arg _ hx) (coe_spanSingleton _ x)⟩ }⟩
 #align fractional_ideal.is_principal_iff FractionalIdeal.isPrincipal_iff
 
+/- warning: fractional_ideal.span_singleton_zero -> FractionalIdeal.spanSingleton_zero is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3], Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc (OfNat.ofNat.{u2} P 0 (Zero.toOfNat0.{u2} P (CommMonoidWithZero.toZero.{u2} P (CommSemiring.toCommMonoidWithZero.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))))) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) 0 (Zero.toOfNat0.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instZeroFractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_zero FractionalIdeal.spanSingleton_zeroₓ'. -/
 @[simp]
 theorem spanSingleton_zero : spanSingleton S (0 : P) = 0 :=
   by
@@ -1370,16 +2223,34 @@ theorem spanSingleton_zero : spanSingleton S (0 : P) = 0 :=
   simp [Submodule.mem_span_singleton, eq_comm]
 #align fractional_ideal.span_singleton_zero FractionalIdeal.spanSingleton_zero
 
+/- warning: fractional_ideal.span_singleton_eq_zero_iff -> FractionalIdeal.spanSingleton_eq_zero_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_eq_zero_iff FractionalIdeal.spanSingleton_eq_zero_iffₓ'. -/
 theorem spanSingleton_eq_zero_iff {y : P} : spanSingleton S y = 0 ↔ y = 0 :=
   ⟨fun h =>
     span_eq_bot.mp (by simpa using congr_arg Subtype.val h : span R {y} = ⊥) y (mem_singleton y),
     fun h => by simp [h]⟩
 #align fractional_ideal.span_singleton_eq_zero_iff FractionalIdeal.spanSingleton_eq_zero_iff
 
+/- warning: fractional_ideal.span_singleton_ne_zero_iff -> FractionalIdeal.spanSingleton_ne_zero_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_ne_zero_iff FractionalIdeal.spanSingleton_ne_zero_iffₓ'. -/
 theorem spanSingleton_ne_zero_iff {y : P} : spanSingleton S y ≠ 0 ↔ y ≠ 0 :=
   not_congr spanSingleton_eq_zero_iff
 #align fractional_ideal.span_singleton_ne_zero_iff FractionalIdeal.spanSingleton_ne_zero_iff
 
+/- warning: fractional_ideal.span_singleton_one -> FractionalIdeal.spanSingleton_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_one FractionalIdeal.spanSingleton_oneₓ'. -/
 @[simp]
 theorem spanSingleton_one : spanSingleton S (1 : P) = 1 :=
   by
@@ -1389,6 +2260,12 @@ theorem spanSingleton_one : spanSingleton S (1 : P) = 1 :=
   rw [Algebra.smul_def, mul_one]
 #align fractional_ideal.span_singleton_one FractionalIdeal.spanSingleton_one
 
+/- warning: fractional_ideal.span_singleton_mul_span_singleton -> FractionalIdeal.spanSingleton_mul_spanSingleton is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_mul_span_singleton FractionalIdeal.spanSingleton_mul_spanSingletonₓ'. -/
 @[simp]
 theorem spanSingleton_mul_spanSingleton (x y : P) :
     spanSingleton S x * spanSingleton S y = spanSingleton S (x * y) :=
@@ -1397,6 +2274,12 @@ theorem spanSingleton_mul_spanSingleton (x y : P) :
   simp only [coe_mul, coe_span_singleton, span_mul_span, singleton_mul_singleton]
 #align fractional_ideal.span_singleton_mul_span_singleton FractionalIdeal.spanSingleton_mul_spanSingleton
 
+/- warning: fractional_ideal.span_singleton_pow -> FractionalIdeal.spanSingleton_pow is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_pow FractionalIdeal.spanSingleton_powₓ'. -/
 @[simp]
 theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingleton S (x ^ n) :=
   by
@@ -1405,8 +2288,14 @@ theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingle
   · rw [pow_succ, hn, span_singleton_mul_span_singleton, pow_succ]
 #align fractional_ideal.span_singleton_pow FractionalIdeal.spanSingleton_pow
 
+/- warning: fractional_ideal.coe_ideal_span_singleton -> FractionalIdeal.coeIdeal_span_singleton is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (x : R), Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.coeIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (Ideal.span.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Singleton.singleton.{u1, u1} R (Set.{u1} R) (Set.instSingletonSet.{u1} R) x))) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) x) _inst_2 _inst_3 loc (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => P) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) R P (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) R P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)))) R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u2} R P (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} P (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2))))))) (algebraMap.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} P (CommRing.toCommSemiring.{u2} P _inst_2)) _inst_3) x))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coeIdeal_span_singletonₓ'. -/
 @[simp]
-theorem coe_ideal_spanSingleton (x : R) :
+theorem coeIdeal_span_singleton (x : R) :
     (↑(Ideal.span {x} : Ideal R) : FractionalIdeal S P) = spanSingleton S (algebraMap R P x) :=
   by
   ext y
@@ -1419,8 +2308,14 @@ theorem coe_ideal_spanSingleton (x : R) :
   · rintro ⟨y', rfl⟩
     refine' ⟨y' * x, submodule.mem_span_singleton.mpr ⟨y', rfl⟩, _⟩
     rw [RingHom.map_mul, Algebra.smul_def]
-#align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coe_ideal_spanSingleton
-
+#align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coeIdeal_span_singleton
+
+/- warning: fractional_ideal.canonical_equiv_span_singleton -> FractionalIdeal.canonicalEquiv_spanSingleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {P' : Type.{u3}} [_inst_8 : CommRing.{u3} P'] [_inst_9 : Algebra.{u1, u3} R P' (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} P' (CommRing.toRing.{u3} P' _inst_8))] [_inst_10 : IsLocalization.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) S P' (CommRing.toCommSemiring.{u3} P' _inst_8) _inst_9] (x : P), Eq.{succ u3} (FractionalIdeal.{u1, u3} R _inst_1 S P' _inst_8 _inst_9) (coeFn.{max (succ u2) (succ u3), max 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(Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) => R -> R) (RingHom.hasCoeToFun.{u1, u1} R R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R 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+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {P' : Type.{u3}} [_inst_8 : CommRing.{u3} P'] [_inst_9 : Algebra.{u2, u3} R P' (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} P' (CommRing.toCommSemiring.{u3} P' _inst_8))] [_inst_10 : IsLocalization.{u2, u3} R (CommRing.toCommSemiring.{u2} R _inst_1) S P' (CommRing.toCommSemiring.{u3} P' _inst_8) _inst_9] (x : P), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingletonₓ'. -/
 @[simp]
 theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocalization S P']
     (x : P) :
@@ -1445,6 +2340,12 @@ theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocali
     simp [IsLocalization.map_smul]
 #align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingleton
 
+/- warning: fractional_ideal.mem_singleton_mul -> FractionalIdeal.mem_singleton_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {x : P} {y : P} {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) y (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc x) I)) (Exists.{succ u2} P (fun (y' : P) => Exists.{0} (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) y' I) (fun (H : Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) y' I) => Eq.{succ u2} P y (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) x y'))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {x : P} {y : P} {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) y (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc x) I)) (Exists.{succ u1} P (fun (y' : P) => And (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) y' I) (Eq.{succ u1} P y (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) x y'))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mem_singleton_mul FractionalIdeal.mem_singleton_mulₓ'. -/
 theorem mem_singleton_mul {x y : P} {I : FractionalIdeal S P} :
     y ∈ spanSingleton S x * I ↔ ∃ y' ∈ I, y = x * y' :=
   by
@@ -1465,7 +2366,13 @@ omit loc
 
 variable (K)
 
-theorem mk'_mul_coe_ideal_eq_coe_ideal {I J : Ideal R₁} {x y : R₁} (hy : y ∈ R₁⁰) :
+/- warning: fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal -> FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] (K : Type.{u2}) [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] {I : Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))} {J : Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))} {x : R₁} {y : R₁} (hy : Membership.Mem.{u1, u1} R₁ (Submonoid.{u1} R₁ (MulZeroOneClass.toMulOneClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R₁ (MulZeroOneClass.toMulOneClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))))) R₁ (Submonoid.setLike.{u1} R₁ (MulZeroOneClass.toMulOneClass.{u1} R₁ (MonoidWithZero.toMulZeroOneClass.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))))))) y (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))))), Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ 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(CommRing.toRing.{u1} R₁ _inst_4))) (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (instHMul.{u1} (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (Ideal.hasMul.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Ideal.span.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (Singleton.singleton.{u1, u1} R₁ (Set.{u1} R₁) (Set.hasSingleton.{u1} R₁) y)) J))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] (K : Type.{u1}) [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [_inst_7 : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] {I : Ideal.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))} {J : Ideal.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))} {x : R₁} {y : R₁} (hy : Membership.mem.{u2, u2} R₁ (Submonoid.{u2} R₁ (MulZeroOneClass.toMulOneClass.{u2} R₁ (MonoidWithZero.toMulZeroOneClass.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} R₁ (MulZeroOneClass.toMulOneClass.{u2} R₁ 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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdealₓ'. -/
+theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈ R₁⁰) :
     spanSingleton R₁⁰ (IsLocalization.mk' K x ⟨y, hy⟩) * I = (J : FractionalIdeal R₁⁰ K) ↔
       Ideal.span {x} * I = Ideal.span {y} * J :=
   by
@@ -1483,25 +2390,43 @@ theorem mk'_mul_coe_ideal_eq_coe_ideal {I J : Ideal R₁} {x y : R₁} (hy : y 
     mul_assoc, span_singleton_mul_span_singleton, ← mul_assoc, span_singleton_mul_span_singleton,
     mul_comm (mk' _ _ _), ← IsLocalization.mk'_eq_mul_mk'_one, mul_comm (mk' _ _ _), ←
     IsLocalization.mk'_eq_mul_mk'_one, IsLocalization.mk'_self, span_singleton_one, one_mul]
-#align fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal FractionalIdeal.mk'_mul_coe_ideal_eq_coe_ideal
+#align fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal
 
 variable {K}
 
-theorem spanSingleton_mul_coe_ideal_eq_coe_ideal {I J : Ideal R₁} {z : K} :
+/- warning: fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal -> FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] {I : Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))} {J : Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))} {z : K}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdealₓ'. -/
+theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
     spanSingleton R₁⁰ z * (I : FractionalIdeal R₁⁰ K) = J ↔
       Ideal.span {((IsLocalization.sec R₁⁰ z).1 : R₁)} * I =
         Ideal.span {(IsLocalization.sec R₁⁰ z).2} * J :=
   by-- `erw` to deal with the distinction between `y` and `⟨y.1, y.2⟩`
   erw [← mk'_mul_coe_ideal_eq_coe_ideal K (IsLocalization.sec R₁⁰ z).2.Prop,
     IsLocalization.mk'_sec K z]
-#align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coe_ideal_eq_coe_ideal
+#align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal
 
 variable [IsDomain R₁]
 
+/- warning: fractional_ideal.one_div_span_singleton -> FractionalIdeal.one_div_spanSingleton is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_8 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] (x : K), Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 _inst_8)) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.one.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasOne.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 _inst_7 x)) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 _inst_7 (Inv.inv.{u2} K (DivInvMonoid.toHasInv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) x))
+but is expected to have type
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_8 : IsDomain.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))] (x : K), Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 _inst_8)) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 1 (One.toOfNat1.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.instOneFractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 _inst_7 x)) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 _inst_7 (Inv.inv.{u2} K (Field.toInv.{u2} K _inst_5) x))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.one_div_span_singleton FractionalIdeal.one_div_spanSingletonₓ'. -/
 theorem one_div_spanSingleton (x : K) : 1 / spanSingleton R₁⁰ x = spanSingleton R₁⁰ x⁻¹ :=
   if h : x = 0 then by simp [h] else (eq_one_div_of_mul_eq_one_right _ _ (by simp [h])).symm
 #align fractional_ideal.one_div_span_singleton FractionalIdeal.one_div_spanSingleton
 
+/- warning: fractional_ideal.div_span_singleton -> FractionalIdeal.div_spanSingleton is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_8 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] (J : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (d : K), Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HDiv.hDiv.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHDiv.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasDiv.{u1, u2} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 _inst_8)) J (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 _inst_7 d)) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 _inst_7 (Inv.inv.{u2} K (DivInvMonoid.toHasInv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) d)) J)
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [_inst_7 : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_8 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] (J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (d : K), Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (HDiv.hDiv.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHDiv.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instDivFractionalIdealNonZeroDivisorsToMonoidWithZeroToSemiringToCommSemiringToCommRingToEuclideanDomain.{u2, u1} R₁ _inst_4 K _inst_5 _inst_6 _inst_7 _inst_8)) J (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 _inst_7 d)) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 _inst_7 (Inv.inv.{u1} K (Field.toInv.{u1} K _inst_5) d)) J)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingletonₓ'. -/
 @[simp]
 theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
     J / spanSingleton R₁⁰ d = spanSingleton R₁⁰ d⁻¹ * J :=
@@ -1522,6 +2447,12 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
     exact le_refl J
 #align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingleton
 
+/- warning: fractional_ideal.exists_eq_span_singleton_mul -> FractionalIdeal.exists_eq_spanSingleton_mul is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_8 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6), Exists.{succ u1} R₁ (fun (a : R₁) => Exists.{succ u1} (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (fun (aI : Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) => And (Ne.{succ u1} R₁ a (OfNat.ofNat.{u1} R₁ 0 (OfNat.mk.{u1} R₁ 0 (Zero.zero.{u1} R₁ (MulZeroClass.toHasZero.{u1} R₁ (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R₁ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R₁ (NonAssocRing.toNonUnitalNonAssocRing.{u1} R₁ (Ring.toNonAssocRing.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))))))))) (Eq.{succ u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) I (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 _inst_7 (Inv.inv.{u2} K (DivInvMonoid.toHasInv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) (fun (_x : RingHom.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) => R₁ -> K) (RingHom.hasCoeToFun.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) (algebraMap.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6) a))) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (CoeTCₓ.coe.{succ u1, succ u2} (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))) aI)))))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [_inst_7 : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_8 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] (I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6), Exists.{succ u2} R₁ (fun (a : R₁) => Exists.{succ u2} (Ideal.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (fun (aI : Ideal.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) => And (Ne.{succ u2} R₁ a (OfNat.ofNat.{u2} R₁ 0 (Zero.toOfNat0.{u2} R₁ (CommMonoidWithZero.toZero.{u2} R₁ (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} R₁ (IsDomain.toCancelCommMonoidWithZero.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4) _inst_8)))))) (Eq.{succ u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) I (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) _inst_5)) _inst_6 _inst_7 (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonUnitalNonAssocSemiring.toMul.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))))) (algebraMap.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6) a))) (FractionalIdeal.coeIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 aI)))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mulₓ'. -/
 theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
     ∃ (a : R₁)(aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI :=
   by
@@ -1546,6 +2477,7 @@ theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
     rwa [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
 #align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mul
 
+#print FractionalIdeal.isPrincipal /-
 instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Algebra R K]
     [IsFractionRing R K] (I : FractionalIdeal R⁰ K) : (I : Submodule R K).IsPrincipal :=
   by
@@ -1559,15 +2491,28 @@ instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Alg
   rw [Ideal.submodule_span_eq, coe_ideal_span_singleton (generator aI),
     span_singleton_mul_span_singleton]
 #align fractional_ideal.is_principal FractionalIdeal.isPrincipal
+-/
 
 include loc
 
+/- warning: fractional_ideal.le_span_singleton_mul_iff -> FractionalIdeal.le_spanSingleton_mul_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) I (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc x) J)) (forall (zI : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) zI I) -> (Exists.{succ u2} P (fun (zJ : P) => Exists.{0} (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) zJ J) (fun (H : Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) zJ J) => Eq.{succ u2} P (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) x zJ) zI))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) I (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc x) J)) (forall (zI : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) zI I) -> (Exists.{succ u1} P (fun (zJ : P) => And (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) zJ J) (Eq.{succ u1} P (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) x zJ) zI))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.le_span_singleton_mul_iff FractionalIdeal.le_spanSingleton_mul_iffₓ'. -/
 theorem le_spanSingleton_mul_iff {x : P} {I J : FractionalIdeal S P} :
     I ≤ spanSingleton S x * J ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI :=
   show (∀ {zI} (hzI : zI ∈ I), zI ∈ spanSingleton _ x * J) ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI by
     simp only [mem_singleton_mul, eq_comm]
 #align fractional_ideal.le_span_singleton_mul_iff FractionalIdeal.le_spanSingleton_mul_iff
 
+/- warning: fractional_ideal.span_singleton_mul_le_iff -> FractionalIdeal.spanSingleton_mul_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (Preorder.toHasLe.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc x) I) J) (forall (z : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) z I) -> (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) x z) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (LE.le.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.lattice.{u2, u1} R _inst_1 S P _inst_2 _inst_3))))) (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc x) I) J) (forall (z : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) z I) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) x z) J))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.span_singleton_mul_le_iff FractionalIdeal.spanSingleton_mul_le_iffₓ'. -/
 theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
     spanSingleton _ x * I ≤ J ↔ ∀ z ∈ I, x * z ∈ J :=
   by
@@ -1580,6 +2525,12 @@ theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
     exact Submodule.smul_mem J.1 _ (h zI hzI)
 #align fractional_ideal.span_singleton_mul_le_iff FractionalIdeal.spanSingleton_mul_le_iff
 
+/- warning: fractional_ideal.eq_span_singleton_mul -> FractionalIdeal.eq_spanSingleton_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))} {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) I (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.hasMul.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u1, u2} R _inst_1 S P _inst_2 _inst_3 loc x) J)) (And (forall (zI : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) zI I) -> (Exists.{succ u2} P (fun (zJ : P) => Exists.{0} (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) zJ J) (fun (H : Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) zJ J) => Eq.{succ u2} P (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) x zJ) zI)))) (forall (z : P), (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) z J) -> (Membership.Mem.{u2, u2} P (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (FractionalIdeal.{u1, u2} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.setLike.{u1, u2} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} P P P (instHMul.{u2} P (Distrib.toHasMul.{u2} P (Ring.toDistrib.{u2} P (CommRing.toRing.{u2} P _inst_2)))) x z) I)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] {S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))} {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] {x : P} {I : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3} {J : FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3}, Iff (Eq.{succ u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) I (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (instHMul.{u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (FractionalIdeal.spanSingleton.{u2, u1} R _inst_1 S P _inst_2 _inst_3 loc x) J)) (And (forall (zI : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) zI I) -> (Exists.{succ u1} P (fun (zJ : P) => And (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) zJ J) (Eq.{succ u1} P (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) x zJ) zI)))) (forall (z : P), (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) z J) -> (Membership.mem.{u1, u1} P (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) (SetLike.instMembership.{u1, u1} (FractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3) P (FractionalIdeal.instSetLikeFractionalIdeal.{u2, u1} R _inst_1 S P _inst_2 _inst_3)) (HMul.hMul.{u1, u1, u1} P P P (instHMul.{u1} P (NonUnitalNonAssocRing.toMul.{u1} P (NonAssocRing.toNonUnitalNonAssocRing.{u1} P (Ring.toNonAssocRing.{u1} P (CommRing.toRing.{u1} P _inst_2))))) x z) I)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.eq_span_singleton_mul FractionalIdeal.eq_spanSingleton_mulₓ'. -/
 theorem eq_spanSingleton_mul {x : P} {I J : FractionalIdeal S P} :
     I = spanSingleton _ x * J ↔ (∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI) ∧ ∀ z ∈ J, x * z ∈ I := by
   simp only [le_antisymm_iff, le_span_singleton_mul_iff, span_singleton_mul_le_iff]
@@ -1593,6 +2544,12 @@ variable {K : Type _} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
 attribute [local instance] Classical.propDecidable
 
+/- warning: fractional_ideal.is_noetherian_zero -> FractionalIdeal.isNoetherian_zero is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))], IsNoetherian.{u1, u2} R₁ (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ 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(Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))))) (FractionalIdeal.addCommGroup.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 (OfNat.ofNat.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} 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(Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (OfNat.mk.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) 0 (Zero.zero.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasZero.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))], IsNoetherian.{u2, u1} R₁ (Subtype.{succ u1} K (fun (x : K) => Membership.mem.{u1, u1} K (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) K (Submodule.setLike.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6))) x (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6)))))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (OfNat.ofNat.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) 0 (Zero.toOfNat0.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.instZeroFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zeroₓ'. -/
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
   isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) =>
     by
@@ -1601,24 +2558,42 @@ theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
     exact fg_bot
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 
+/- warning: fractional_ideal.is_noetherian_iff -> FractionalIdeal.isNoetherian_iff is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, Iff (IsNoetherian.{u1, u2} R₁ (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ 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(CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6)) (FractionalIdeal.Submodule.hasCoe.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)))) J)))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, Iff (IsNoetherian.{u2, u1} R₁ (Subtype.{succ u1} K (fun (x : K) => Membership.mem.{u1, u1} K (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) K (Submodule.setLike.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6))) x (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)) (forall (J : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6), (LE.le.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Preorder.toLE.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (PartialOrder.toPreorder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (SemilatticeInf.toPartialOrder.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (Lattice.toSemilatticeInf.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.lattice.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6))))) J I) -> (Submodule.FG.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 J)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iffₓ'. -/
 theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
     IsNoetherian R₁ I ↔ ∀ J ≤ I, (J : Submodule R₁ K).FG :=
   isNoetherian_submodule.trans ⟨fun h J hJ => h _ hJ, fun h J hJ => h ⟨J, isFractional_of_le hJ⟩ hJ⟩
 #align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iff
 
-theorem isNoetherian_coe_ideal [IsNoetherianRing R₁] (I : Ideal R₁) :
+/- warning: fractional_ideal.is_noetherian_coe_ideal -> FractionalIdeal.isNoetherian_coeIdeal is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [_inst_7 : IsNoetherianRing.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] (I : Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))), IsNoetherian.{u1, u2} R₁ (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) ((fun (a : Type.{u1}) (b : Type.{u2}) [self : HasLiftT.{succ u1, succ u2} a b] => self.0) (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (HasLiftT.mk.{succ u1, succ u2} (Ideal.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K 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(Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasCoeT.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6))) I))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [_inst_7 : IsNoetherianRing.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] (I : Ideal.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))), IsNoetherian.{u2, u1} R₁ (Subtype.{succ u1} K (fun (x : K) => Membership.mem.{u1, u1} K (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) K (Submodule.setLike.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6))) x (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (FractionalIdeal.coeIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (FractionalIdeal.coeIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 (FractionalIdeal.coeIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_coe_ideal FractionalIdeal.isNoetherian_coeIdealₓ'. -/
+theorem isNoetherian_coeIdeal [IsNoetherianRing R₁] (I : Ideal R₁) :
     IsNoetherian R₁ (I : FractionalIdeal R₁⁰ K) :=
   by
   rw [is_noetherian_iff]
   intro J hJ
   obtain ⟨J, rfl⟩ := le_one_iff_exists_coe_ideal.mp (le_trans hJ coe_ideal_le_one)
   exact (IsNoetherian.noetherian J).map _
-#align fractional_ideal.is_noetherian_coe_ideal FractionalIdeal.isNoetherian_coe_ideal
+#align fractional_ideal.is_noetherian_coe_ideal FractionalIdeal.isNoetherian_coeIdeal
 
 include frac
 
 variable [IsDomain R₁]
 
+/- warning: fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul -> FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] (x : R₁) {I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6}, (IsNoetherian.{u1, u2} R₁ (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I) (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I) (FractionalIdeal.addCommGroup.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 I)) (FractionalIdeal.module.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K 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(nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 frac (Inv.inv.{u2} K (DivInvMonoid.toHasInv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) (fun (_x : RingHom.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) => R₁ -> K) (RingHom.hasCoeToFun.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) (algebraMap.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6) x))) I))) (FractionalIdeal.module.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 (HMul.hMul.{u2, u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (instHMul.{u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) (FractionalIdeal.hasMul.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 frac (Inv.inv.{u2} K (DivInvMonoid.toHasInv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) (fun (_x : RingHom.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) => R₁ -> K) (RingHom.hasCoeToFun.{u1, u2} R₁ K (Semiring.toNonAssocSemiring.{u1} R₁ (CommSemiring.toSemiring.{u1} R₁ (CommRing.toCommSemiring.{u1} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))))) (algebraMap.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5))) _inst_6) x))) I)))
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] (x : R₁) {I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6}, (IsNoetherian.{u2, u1} R₁ (Subtype.{succ u1} K (fun (x : K) => Membership.mem.{u1, u1} K (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) K (Submodule.setLike.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6))) x (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)) -> (IsNoetherian.{u2, u1} R₁ (Subtype.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (fun (x_1 : K) => Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Submodule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)))) _inst_6)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)))) _inst_6)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Submodule.setLike.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)))) _inst_6))) x_1 (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 frac (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ (fun (a : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonUnitalNonAssocSemiring.toMul.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))))) (algebraMap.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6) x))) I)))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 frac (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonUnitalNonAssocSemiring.toMul.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))))) (algebraMap.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6) x))) I))) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 (HMul.hMul.{u1, u1, u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6) (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (instHMul.{u1} (FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6) (FractionalIdeal.instMulFractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6)) (FractionalIdeal.spanSingleton.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (EuclideanDomain.toCommRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toEuclideanDomain.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5)) _inst_6 frac (Inv.inv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) (Field.toInv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) x) _inst_5) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ (fun (_x : R₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R₁) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonUnitalNonAssocSemiring.toMul.{u2} R₁ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R₁ (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))))) R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))) (RingHom.instRingHomClassRingHom.{u2, u1} R₁ K (Semiring.toNonAssocSemiring.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))))))) (algebraMap.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5))) _inst_6) x))) I)))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mulₓ'. -/
 theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdeal R₁⁰ K}
     (hI : IsNoetherian R₁ I) :
     IsNoetherian R₁ (spanSingleton R₁⁰ (algebraMap R₁ K x)⁻¹ * I : FractionalIdeal R₁⁰ K) :=
@@ -1639,6 +2614,12 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
     mul_one]
 #align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul
 
+/- warning: fractional_ideal.is_noetherian -> FractionalIdeal.isNoetherian is a dubious translation:
+lean 3 declaration is
+  forall {R₁ : Type.{u1}} [_inst_4 : CommRing.{u1} R₁] {K : Type.{u2}} [_inst_5 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} R₁ K (CommRing.toCommSemiring.{u1} R₁ _inst_4) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_5)))] [frac : IsFractionRing.{u1, u2} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] [_inst_8 : IsNoetherianRing.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4))] (I : FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6), IsNoetherian.{u1, u2} R₁ (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I) (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)) (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (FractionalIdeal.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6) K (FractionalIdeal.setLike.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6)) I) (FractionalIdeal.addCommGroup.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 I)) (FractionalIdeal.module.{u1, u2} R₁ _inst_4 (nonZeroDivisors.{u1} R₁ (Semiring.toMonoidWithZero.{u1} R₁ (Ring.toSemiring.{u1} R₁ (CommRing.toRing.{u1} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_5)) _inst_6 I)
+but is expected to have type
+  forall {R₁ : Type.{u2}} [_inst_4 : CommRing.{u2} R₁] {K : Type.{u1}} [_inst_5 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_5)))] [frac : IsFractionRing.{u2, u1} R₁ _inst_4 K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6] [_inst_7 : IsDomain.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] [_inst_8 : IsNoetherianRing.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4))] (I : FractionalIdeal.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6), IsNoetherian.{u2, u1} R₁ (Subtype.{succ u1} K (fun (x : K) => Membership.mem.{u1, u1} K (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6)) K (Submodule.setLike.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6))) x (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I))) (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (Submodule.addCommMonoid.{u2, u1} R₁ K (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (CommRing.toRing.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5))))))) (Algebra.toModule.{u2, u1} R₁ K (CommRing.toCommSemiring.{u2} R₁ _inst_4) (CommSemiring.toSemiring.{u1} K (CommRing.toCommSemiring.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)))) _inst_6) (FractionalIdeal.coeToSubmodule.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)) (FractionalIdeal.instModuleSubtypeMemSubmoduleToSemiringToCommSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingToRingToModuleToSemiringToCommSemiringInstMembershipSetLikeCoeToSubmoduleAddCommMonoid.{u2, u1} R₁ _inst_4 (nonZeroDivisors.{u2} R₁ (Semiring.toMonoidWithZero.{u2} R₁ (CommSemiring.toSemiring.{u2} R₁ (CommRing.toCommSemiring.{u2} R₁ _inst_4)))) K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_5)) _inst_6 I)
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_noetherian FractionalIdeal.isNoetherianₓ'. -/
 /-- Every fractional ideal of a noetherian integral domain is noetherian. -/
 theorem isNoetherian [IsNoetherianRing R₁] (I : FractionalIdeal R₁⁰ K) : IsNoetherian R₁ I :=
   by
@@ -1655,22 +2636,32 @@ omit frac
 
 variable {R P} (S) (x : P) (hx : IsIntegral R x)
 
+/- warning: fractional_ideal.is_fractional_adjoin_integral -> FractionalIdeal.isFractional_adjoin_integral is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) {P : Type.{u2}} [_inst_2 : CommRing.{u2} P] [_inst_3 : Algebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))] [loc : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S P (CommRing.toCommSemiring.{u2} P _inst_2) _inst_3] (x : P), (IsIntegral.{u1, u2} R P _inst_1 (CommRing.toRing.{u2} P _inst_2) _inst_3 x) -> (IsFractional.{u1, u2} R _inst_1 S P _inst_2 _inst_3 (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) P (Subalgebra.setLike.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))) (Preorder.toHasLe.{u2} 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(Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))))))) => (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) -> (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) P (Subalgebra.setLike.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u1, u2} R P (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} P (Semiring.toNonAssocSemiring.{u2} P (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2))))) (Algebra.toModule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3) (Algebra.adjoin.{u1, u2} R P (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} P (CommRing.toRing.{u2} P _inst_2)) _inst_3 (Singleton.singleton.{u2, u2} P (Set.{u2} P) (Set.hasSingleton.{u2} P) x))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (S : Submonoid.{u2} R (MulZeroOneClass.toMulOneClass.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) {P : Type.{u1}} [_inst_2 : CommRing.{u1} P] [_inst_3 : Algebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))] [loc : IsLocalization.{u2, u1} R (CommRing.toCommSemiring.{u2} R _inst_1) S P (CommRing.toCommSemiring.{u1} P _inst_2) _inst_3] (x : P), (IsIntegral.{u2, u1} R P _inst_1 (CommRing.toRing.{u1} P _inst_2) _inst_3 x) -> (IsFractional.{u2, u1} R _inst_1 S P _inst_2 _inst_3 (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) P (Subalgebra.instSetLikeSubalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3))))))) (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (fun (_x : Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) => Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) P (Subalgebra.instSetLikeSubalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3))))))) (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P 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(Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) P (Subalgebra.instSetLikeSubalgebra.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)) (Submodule.completeLattice.{u2, u1} R P (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} P (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} P (Semiring.toNonAssocSemiring.{u1} P (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2))))) (Algebra.toModule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3) (Algebra.adjoin.{u2, u1} R P (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} P (CommRing.toCommSemiring.{u1} P _inst_2)) _inst_3 (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) x))))
+Case conversion may be inaccurate. Consider using '#align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integralₓ'. -/
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Algebra.adjoin R ({x} : Set P)).toSubmodule :=
-  isFractional_of_fG (FG_adjoin_singleton_of_integral x hx)
+  isFractional_of_fg (FG_adjoin_singleton_of_integral x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 
+#print FractionalIdeal.adjoinIntegral /-
 /-- `fractional_ideal.adjoin_integral (S : submonoid R) x hx` is `R[x]` as a fractional ideal,
 where `hx` is a proof that `x : P` is integral over `R`. -/
 @[simps]
 def adjoinIntegral : FractionalIdeal S P :=
   ⟨_, isFractional_adjoin_integral S x hx⟩
 #align fractional_ideal.adjoin_integral FractionalIdeal.adjoinIntegral
+-/
 
+#print FractionalIdeal.mem_adjoinIntegral_self /-
 theorem mem_adjoinIntegral_self : x ∈ adjoinIntegral S x hx :=
   Algebra.subset_adjoin (Set.mem_singleton x)
 #align fractional_ideal.mem_adjoin_integral_self FractionalIdeal.mem_adjoinIntegral_self
+-/
 
 end Adjoin
 

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

@@ -1658,7 +1658,7 @@ variable {R P} (S) (x : P) (hx : IsIntegral R x)
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Algebra.adjoin R ({x} : Set P)).toSubmodule :=
-  isFractional_of_fG (fG_adjoin_singleton_of_integral x hx)
+  isFractional_of_fG (FG_adjoin_singleton_of_integral x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 
 /-- `fractional_ideal.adjoin_integral (S : submonoid R) x hx` is `R[x]` as a fractional ideal,

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -853,13 +853,13 @@ theorem isFractional_span_iff {s : Set P} :
 
 include loc
 
-theorem isFractional_of_fg {I : Submodule R P} (hI : I.Fg) : IsFractional S I :=
+theorem isFractional_of_fG {I : Submodule R P} (hI : I.FG) : IsFractional S I :=
   by
   rcases hI with ⟨I, rfl⟩
   rcases exist_integer_multiples_of_finset S I with ⟨⟨s, hs1⟩, hs⟩
   rw [is_fractional_span_iff]
   exact ⟨s, hs1, hs⟩
-#align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fg
+#align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fG
 
 omit loc
 
@@ -870,27 +870,27 @@ theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx :
 
 variable (S)
 
-theorem coe_ideal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
-    Fg ((I : FractionalIdeal S P) : Submodule R P) ↔ I.Fg :=
+theorem coe_ideal_fG (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
+    FG ((I : FractionalIdeal S P) : Submodule R P) ↔ I.FG :=
   coeSubmodule_fg _ inj _
-#align fractional_ideal.coe_ideal_fg FractionalIdeal.coe_ideal_fg
+#align fractional_ideal.coe_ideal_fg FractionalIdeal.coe_ideal_fG
 
 variable {S}
 
-theorem fg_unit (I : (FractionalIdeal S P)ˣ) : Fg (I : Submodule R P) :=
+theorem fG_unit (I : (FractionalIdeal S P)ˣ) : FG (I : Submodule R P) :=
   Submodule.fg_unit <| Units.map (coeSubmoduleHom S P).toMonoidHom I
-#align fractional_ideal.fg_unit FractionalIdeal.fg_unit
+#align fractional_ideal.fg_unit FractionalIdeal.fG_unit
 
-theorem fg_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : Fg (I : Submodule R P) :=
-  fg_unit h.Unit
-#align fractional_ideal.fg_of_is_unit FractionalIdeal.fg_of_isUnit
+theorem fG_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : FG (I : Submodule R P) :=
+  fG_unit h.Unit
+#align fractional_ideal.fg_of_is_unit FractionalIdeal.fG_of_isUnit
 
-theorem Ideal.fg_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
-    (h : IsUnit (I : FractionalIdeal S P)) : I.Fg :=
+theorem Ideal.fG_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
+    (h : IsUnit (I : FractionalIdeal S P)) : I.FG :=
   by
   rw [← coe_ideal_fg S inj I]
   exact fg_of_is_unit I h
-#align ideal.fg_of_is_unit Ideal.fg_of_isUnit
+#align ideal.fg_of_is_unit Ideal.fG_of_isUnit
 
 variable (S P P')
 
@@ -1602,7 +1602,7 @@ theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 
 theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
-    IsNoetherian R₁ I ↔ ∀ J ≤ I, (J : Submodule R₁ K).Fg :=
+    IsNoetherian R₁ I ↔ ∀ J ≤ I, (J : Submodule R₁ K).FG :=
   isNoetherian_submodule.trans ⟨fun h J hJ => h _ hJ, fun h J hJ => h ⟨J, isFractional_of_le hJ⟩ hJ⟩
 #align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iff
 
@@ -1658,7 +1658,7 @@ variable {R P} (S) (x : P) (hx : IsIntegral R x)
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Algebra.adjoin R ({x} : Set P)).toSubmodule :=
-  isFractional_of_fg (fg_adjoin_singleton_of_integral x hx)
+  isFractional_of_fG (fG_adjoin_singleton_of_integral x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 
 /-- `fractional_ideal.adjoin_integral (S : submonoid R) x hx` is `R[x]` as a fractional ideal,

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

@@ -923,7 +923,7 @@ theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P'
   RingEquiv.ext fun I =>
     SetLike.ext_iff.mpr fun x =>
       by
-      rw [mem_canonical_equiv_apply, canonical_equiv, map_equiv_symm, map_equiv, [anonymous],
+      rw [mem_canonical_equiv_apply, canonical_equiv, map_equiv_symm, map_equiv, RingEquiv.coe_mk,
         mem_map]
       exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
 #align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symm

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

@@ -477,7 +477,7 @@ theorem IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
   | 0, _ => by
     rw [zero_smul]
-    convert ((0 : Ideal R) : FractionalIdeal S P).IsFractional
+    convert((0 : Ideal R) : FractionalIdeal S P).IsFractional
     simp
   | n + 1, h => by
     rw [succ_nsmul]
@@ -962,7 +962,7 @@ omit loc'
 theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ :=
   by
   rw [← canonical_equiv_trans_canonical_equiv S P P]
-  convert (canonical_equiv S P P).symm_trans_self
+  convert(canonical_equiv S P P).symm_trans_self
   exact (canonical_equiv_symm S P P).symm
 #align fractional_ideal.canonical_equiv_self FractionalIdeal.canonicalEquiv_self
 

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

@@ -1141,7 +1141,7 @@ theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {
 theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :=
   by
   by_cases hI : I = 0
-  · rw [hI, div_zero, mul_zero]
+  · rw [hI, div_zero, MulZeroClass.mul_zero]
     exact zero_le 1
   · rw [← coe_le_coe, coe_mul, coe_div hI, coe_one]
     apply Submodule.mul_one_div_le_one
@@ -1150,7 +1150,7 @@ theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :
 theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
     I ≤ I * (1 / I) := by
   by_cases hI_nz : I = 0
-  · rw [hI_nz, div_zero, mul_zero]
+  · rw [hI_nz, div_zero, MulZeroClass.mul_zero]
     exact zero_le 0
   · rw [← coe_le_coe, coe_mul, coe_div hI_nz, coe_one]
     rw [← coe_le_coe, coe_one] at hI
@@ -1508,7 +1508,7 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
   by
   rw [← one_div_span_singleton]
   by_cases hd : d = 0
-  · simp only [hd, span_singleton_zero, div_zero, zero_mul]
+  · simp only [hd, span_singleton_zero, div_zero, MulZeroClass.zero_mul]
   have h_spand : span_singleton R₁⁰ d ≠ 0 := mt span_singleton_eq_zero_iff.mp hd
   apply le_antisymm
   · intro x hx
@@ -1624,7 +1624,7 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
     IsNoetherian R₁ (spanSingleton R₁⁰ (algebraMap R₁ K x)⁻¹ * I : FractionalIdeal R₁⁰ K) :=
   by
   by_cases hx : x = 0
-  · rw [hx, RingHom.map_zero, _root_.inv_zero, span_singleton_zero, zero_mul]
+  · rw [hx, RingHom.map_zero, _root_.inv_zero, span_singleton_zero, MulZeroClass.zero_mul]
     exact is_noetherian_zero
   have h_gx : algebraMap R₁ K x ≠ 0 :=
     mt ((injective_iff_map_eq_zero (algebraMap R₁ K)).mp (IsFractionRing.injective _ _) x) hx

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Filippo A. E. Nuccio
 
 ! This file was ported from Lean 3 source module ring_theory.fractional_ideal
-! leanprover-community/mathlib commit 6010cf523816335f7bae7f8584cb2edaace73940
+! leanprover-community/mathlib commit ed90a7d327c3a5caf65a6faf7e8a0d63c4605df7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -605,6 +605,16 @@ instance : CommSemiring (FractionalIdeal S P) :=
   Function.Injective.commSemiring coe Subtype.coe_injective coe_zero coe_one coe_add coe_mul
     (fun _ _ => coe_nsmul _ _) coe_pow coe_nat_cast
 
+variable (S P)
+
+/-- `fractional_ideal.submodule.has_coe` as a bundled `ring_hom`. -/
+@[simps]
+def coeSubmoduleHom : FractionalIdeal S P →+* Submodule R P :=
+  ⟨coe, coe_one, coe_mul, coe_zero, coe_add⟩
+#align fractional_ideal.coe_submodule_hom FractionalIdeal.coeSubmoduleHom
+
+variable {S P}
+
 section Order
 
 theorem add_le_add_left {I J : FractionalIdeal S P} (hIJ : I ≤ J) (J' : FractionalIdeal S P) :
@@ -868,24 +878,11 @@ theorem coe_ideal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
 variable {S}
 
 theorem fg_unit (I : (FractionalIdeal S P)ˣ) : Fg (I : Submodule R P) :=
-  by
-  have : (1 : P) ∈ (I * ↑I⁻¹ : FractionalIdeal S P) :=
-    by
-    rw [Units.mul_inv]
-    exact one_mem_one _
-  obtain ⟨T, T', hT, hT', one_mem⟩ := mem_span_mul_finite_of_mem_mul this
-  refine' ⟨T, Submodule.span_eq_of_le _ hT _⟩
-  rw [← one_mul ↑I, ← mul_one (span R ↑T)]
-  conv_rhs => rw [← coe_one, ← Units.mul_inv I, coe_mul, mul_comm ↑↑I, ← mul_assoc]
-  refine'
-    Submodule.mul_le_mul_left (le_trans _ (Submodule.mul_le_mul_right (submodule.span_le.mpr hT')))
-  rwa [Submodule.one_le, Submodule.span_mul_span]
+  Submodule.fg_unit <| Units.map (coeSubmoduleHom S P).toMonoidHom I
 #align fractional_ideal.fg_unit FractionalIdeal.fg_unit
 
 theorem fg_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : Fg (I : Submodule R P) :=
-  by
-  rcases h with ⟨I, rfl⟩
-  exact fg_unit I
+  fg_unit h.Unit
 #align fractional_ideal.fg_of_is_unit FractionalIdeal.fg_of_isUnit
 
 theorem Ideal.fg_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -987,7 +987,7 @@ variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ≠ » (0 : R)) -/
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_is_integer [Nontrivial R] (hI : I ≠ 0) :
     ∃ (x : _)(_ : x ≠ (0 : R)), algebraMap R K x ∈ I :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -428,7 +428,7 @@ theorem IsFractional.inf_right {I : Submodule R P} : IsFractional S I → ∀ J,
       exact hI b hbI⟩
 #align is_fractional.inf_right IsFractional.inf_right
 
-instance : HasInf (FractionalIdeal S P) :=
+instance : Inf (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊓ J, I.IsFractional.inf_right J⟩⟩
 
 @[simp, norm_cast]
@@ -436,7 +436,7 @@ theorem coe_inf (I J : FractionalIdeal S P) : ↑(I ⊓ J) = (I ⊓ J : Submodul
   rfl
 #align fractional_ideal.coe_inf FractionalIdeal.coe_inf
 
-instance : HasSup (FractionalIdeal S P) :=
+instance : Sup (FractionalIdeal S P) :=
   ⟨fun I J => ⟨I ⊔ J, I.IsFractional.sup J.IsFractional⟩⟩
 
 @[norm_cast]

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

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

@@ -632,14 +632,14 @@ protected theorem mul_induction_on {I J : FractionalIdeal S P} {C : P → Prop}
 instance : NatCast (FractionalIdeal S P) :=
   ⟨Nat.unaryCast⟩
 
-theorem coe_nat_cast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
+theorem coe_natCast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n :=
   show ((n.unaryCast : FractionalIdeal S P) : Submodule R P) = n
   by induction n <;> simp [*, Nat.unaryCast]
-#align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_cast
+#align fractional_ideal.coe_nat_cast FractionalIdeal.coe_natCast
 
 instance commSemiring : CommSemiring (FractionalIdeal S P) :=
   Function.Injective.commSemiring _ Subtype.coe_injective coe_zero coe_one coe_add coe_mul
-    (fun _ _ => coe_nsmul _ _) coe_pow coe_nat_cast
+    (fun _ _ => coe_nsmul _ _) coe_pow coe_natCast
 
 end Semiring
 

@@ -310,7 +310,7 @@ theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
   have y_ne_zero : y ≠ 0 := by simpa using y_not_mem
   obtain ⟨z, ⟨x, hx⟩⟩ := exists_integer_multiple R⁰ y
   refine' ⟨x, _, _⟩
-  · rw [Ne.def, ← @IsFractionRing.to_map_eq_zero_iff R _ K, hx, Algebra.smul_def]
+  · rw [Ne, ← @IsFractionRing.to_map_eq_zero_iff R _ K, hx, Algebra.smul_def]
     exact mul_ne_zero (IsFractionRing.to_map_ne_zero_of_mem_nonZeroDivisors z.2) y_ne_zero
   · rw [hx]
     exact smul_mem _ _ y_mem

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

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

where the latter is more natural

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

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

but it seems to no longer apply.

Remarks on the PR :

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

@@ -522,7 +522,7 @@ theorem _root_.IsFractional.nsmul {I : Submodule R P} :
     simp
   | n + 1, h => by
     rw [succ_nsmul]
-    exact h.sup (IsFractional.nsmul n h)
+    exact (IsFractional.nsmul n h).sup h
 #align is_fractional.nsmul IsFractional.nsmul
 
 instance : SMul ℕ (FractionalIdeal S P) where smul n I := ⟨n • ↑I, I.isFractional.nsmul n⟩
@@ -551,7 +551,7 @@ theorem _root_.IsFractional.mul {I J : Submodule R P} :
 theorem _root_.IsFractional.pow {I : Submodule R P} (h : IsFractional S I) :
     ∀ n : ℕ, IsFractional S (I ^ n : Submodule R P)
   | 0 => isFractional_of_le_one _ (pow_zero _).le
-  | n + 1 => (pow_succ I n).symm ▸ h.mul (IsFractional.pow h n)
+  | n + 1 => (pow_succ I n).symm ▸ (IsFractional.pow h n).mul h
 #align is_fractional.pow IsFractional.pow
 
 /-- `FractionalIdeal.mul` is the product of two fractional ideals,

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 | |

@@ -554,7 +554,7 @@ theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 := by
     rw [map_div₀, IsFractionRing.mk'_eq_div]
   · rintro ⟨x, rfl⟩
     obtain ⟨y, y_ne, y_mem⟩ := exists_ne_zero_mem_isInteger hI
-    rw [← div_mul_cancel x y_ne, RingHom.map_mul, ← Algebra.smul_def]
+    rw [← div_mul_cancel₀ x y_ne, RingHom.map_mul, ← Algebra.smul_def]
     exact smul_mem (M := L) I (x / y) y_mem
 #align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_one
 

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -40,13 +40,11 @@ namespace FractionalIdeal
 open Set Submodule
 
 variable {R : Type*} [CommRing R] {S : Submonoid R} {P : Type*} [CommRing P]
-
 variable [Algebra R P] [loc : IsLocalization S P]
 
 section
 
 variable {P' : Type*} [CommRing P'] [Algebra R P'] [loc' : IsLocalization S P']
-
 variable {P'' : Type*} [CommRing P''] [Algebra R P''] [loc'' : IsLocalization S P'']
 
 theorem _root_.IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
@@ -301,9 +299,7 @@ i.e. the type `FractionalIdeal R⁰ K` where `IsFractionRing R K`.
 
 
 variable {K K' : Type*} [Field K] [Field K']
-
 variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
-
 variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
 /-- Nonzero fractional ideals contain a nonzero integer. -/
@@ -382,7 +378,6 @@ is a field because `R` is a domain.
 open scoped Classical
 
 variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
-
 variable [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
 instance : Nontrivial (FractionalIdeal R₁⁰ K) :=
@@ -545,7 +540,6 @@ end Quotient
 section Field
 
 variable {R₁ K L : Type*} [CommRing R₁] [Field K] [Field L]
-
 variable [Algebra R₁ K] [IsFractionRing R₁ K] [Algebra K L] [IsFractionRing K L]
 
 theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 := by
@@ -574,7 +568,6 @@ end Field
 section PrincipalIdeal
 
 variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
-
 variable [Algebra R₁ K] [IsFractionRing R₁ K]
 
 open scoped Classical
@@ -899,7 +892,6 @@ theorem num_le (I : FractionalIdeal S P) :
 end PrincipalIdeal
 
 variable {R₁ : Type*} [CommRing R₁]
-
 variable {K : Type*} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
 attribute [local instance] Classical.propDecidable

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -61,9 +61,7 @@ open IsLocalization Pointwise nonZeroDivisors
 section Defs
 
 variable {R : Type*} [CommRing R] {S : Submonoid R} {P : Type*} [CommRing P]
-
 variable [Algebra R P]
-
 variable (S)
 
 /-- A submodule `I` is a fractional ideal if `a I ⊆ R` for some `a ≠ 0`. -/
@@ -90,7 +88,6 @@ namespace FractionalIdeal
 open Set Submodule
 
 variable {R : Type*} [CommRing R] {S : Submonoid R} {P : Type*} [CommRing P]
-
 variable [Algebra R P] [loc : IsLocalization S P]
 
 /-- Map a fractional ideal `I` to a submodule by forgetting that `∃ a, a I ⊆ R`.

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -379,7 +379,7 @@ is a field because `R` is a domain.
 -/
 
 
-open Classical
+open scoped Classical
 
 variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
 
@@ -577,7 +577,7 @@ variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
 
 variable [Algebra R₁ K] [IsFractionRing R₁ K]
 
-open Classical
+open scoped Classical
 
 variable (R₁)
 

Classifies by adding number (#10756) to porting notes claiming added lemma.

@@ -208,7 +208,7 @@ theorem coe_mk (I : Submodule R P) (hI : IsFractional S I) :
   rfl
 #align fractional_ideal.coe_mk FractionalIdeal.coe_mk
 
--- Porting note: added this lemma because Lean can't see through the composition of coercions.
+-- Porting note (#10756): added lemma because Lean can't see through the composition of coercions.
 theorem coeToSet_coeToSubmodule (I : FractionalIdeal S P) :
     ((I : Submodule R P) : Set P) = I :=
   rfl

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>

@@ -504,10 +504,8 @@ theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I := by
 theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) :
     J = 1 / I := by
   have hI : I ≠ 0 := ne_zero_of_mul_eq_one I J h
-  suffices h' : I * (1 / I) = 1
-  · exact
-      congr_arg Units.inv <|
-        @Units.ext _ _ (Units.mkOfMulEqOne _ _ h) (Units.mkOfMulEqOne _ _ h') rfl
+  suffices h' : I * (1 / I) = 1 from
+    congr_arg Units.inv <| @Units.ext _ _ (Units.mkOfMulEqOne _ _ h) (Units.mkOfMulEqOne _ _ h') rfl
   apply le_antisymm
   · apply mul_le.mpr _
     intro x hx y hy

@@ -650,6 +650,7 @@ theorem mem_spanSingleton_self (x : P) : x ∈ spanSingleton S x :=
   (mem_spanSingleton S).mpr ⟨1, one_smul _ _⟩
 #align fractional_ideal.mem_span_singleton_self FractionalIdeal.mem_spanSingleton_self
 
+variable (P) in
 /-- A version of `FractionalIdeal.den_mul_self_eq_num` in terms of fractional ideals. -/
 theorem den_mul_self_eq_num' (I : FractionalIdeal S P) :
     spanSingleton S (algebraMap R P I.den) * I = I.num := by

@@ -116,12 +116,12 @@ protected theorem isFractional (I : FractionalIdeal S P) : IsFractional S (I : S
 #align fractional_ideal.is_fractional FractionalIdeal.isFractional
 
 /-- An element of `S` such that `I.den • I = I.num`, see `FractionalIdeal.num` and
-`FractionalIdeal.den_mul_eq_num`. -/
+`FractionalIdeal.den_mul_self_eq_num`. -/
 noncomputable def den (I : FractionalIdeal S P) : S :=
   ⟨I.2.choose, I.2.choose_spec.1⟩
 
 /-- An ideal of `R` such that `I.den • I = I.num`, see `FractionalIdeal.den` and
-`FractionalIdeal.den_mul_eq_num`. -/
+`FractionalIdeal.den_mul_self_eq_num`. -/
 noncomputable def num (I : FractionalIdeal S P) : Ideal R :=
   (I.den • (I : Submodule R P)).comap (Algebra.linearMap R P)
 

• Add the instances that fractional ideals of number fields are finite and free $\mathbb{Z}$-modules
• For I : (FractionalIdeal (𝓞 K)⁰ K)ˣ with K a number field, define a basis of K that spans I over $\mathbb{Z}$
• Prove that the determinant of that basis over an integral basis of K is the absolute norm of I

@@ -359,6 +359,10 @@ theorem coeIdeal_ne_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 1 ↔ I
   not_iff_not.mpr coeIdeal_eq_one
 #align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coeIdeal_ne_one
 
+theorem num_eq_zero_iff [Nontrivial R] {I : FractionalIdeal R⁰ K} : I.num = 0 ↔ I = 0 :=
+   ⟨fun h ↦ zero_of_num_eq_bot zero_not_mem_nonZeroDivisors h,
+     fun h ↦ h ▸ num_zero_eq (IsFractionRing.injective R K)⟩
+
 end IsFractionRing
 
 section Quotient
@@ -569,7 +573,7 @@ theorem eq_zero_or_one_of_isField (hF : IsField R₁) (I : FractionalIdeal R₁
 
 end Field
 
-section PrincipalIdealRing
+section PrincipalIdeal
 
 variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
 
@@ -886,7 +890,14 @@ theorem eq_spanSingleton_mul {x : P} {I J : FractionalIdeal S P} :
   simp only [le_antisymm_iff, le_spanSingleton_mul_iff, spanSingleton_mul_le_iff]
 #align fractional_ideal.eq_span_singleton_mul FractionalIdeal.eq_spanSingleton_mul
 
-end PrincipalIdealRing
+theorem num_le (I : FractionalIdeal S P) :
+    (I.num : FractionalIdeal S P) ≤ I := by
+  rw [← I.den_mul_self_eq_num', spanSingleton_mul_le_iff]
+  intro _ h
+  rw [← Algebra.smul_def]
+  exact Submodule.smul_mem _ _ h
+
+end PrincipalIdeal
 
 variable {R₁ : Type*} [CommRing R₁]
 

The file RingTheory.FractionalIdeal.Basic is more than 1600 lines long. This PR splits it into two files: Basic and Operations following the model of RingTheory.Ideal.Basic and RingTheory.Ideal.Operations

Co-authored-by: Mario Carneiro <mcarneir@andrew.cmu.edu> Co-authored-by: Jz Pan <acme_pjz@hotmail.com>

The file RingTheory.FractionalIdeal.Basic is more than 1600 lines long. This PR splits it into two files: Basic and Operations following the model of RingTheory.Ideal.Basic and RingTheory.Ideal.Operations

Co-authored-by: Mario Carneiro <mcarneir@andrew.cmu.edu> Co-authored-by: Jz Pan <acme_pjz@hotmail.com>

@@ -3,13 +3,8 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Filippo A. E. Nuccio
 -/
-import Mathlib.Algebra.BigOperators.Finprod
-import Mathlib.RingTheory.IntegralClosure
 import Mathlib.RingTheory.Localization.Integer
 import Mathlib.RingTheory.Localization.Submodule
-import Mathlib.RingTheory.Noetherian
-import Mathlib.RingTheory.PrincipalIdealDomain
-import Mathlib.Tactic.FieldSimp
 
 #align_import ring_theory.fractional_ideal from "leanprover-community/mathlib"@"ed90a7d327c3a5caf65a6faf7e8a0d63c4605df7"
 
@@ -19,26 +14,18 @@ import Mathlib.Tactic.FieldSimp
 This file defines fractional ideals of an integral domain and proves basic facts about them.
 
 ## Main definitions
-Let `S` be a submonoid of an integral domain `R`, `P` the localization of `R` at `S`, and `f` the
-natural ring hom from `R` to `P`.
+Let `S` be a submonoid of an integral domain `R` and `P` the localization of `R` at `S`.
  * `IsFractional` defines which `R`-submodules of `P` are fractional ideals
  * `FractionalIdeal S P` is the type of fractional ideals in `P`
  * a coercion `coeIdeal : Ideal R → FractionalIdeal S P`
  * `CommSemiring (FractionalIdeal S P)` instance:
    the typical ideal operations generalized to fractional ideals
  * `Lattice (FractionalIdeal S P)` instance
- * `map` is the pushforward of a fractional ideal along an algebra morphism
-
-Let `K` be the localization of `R` at `R⁰ = R \ {0}` (i.e. the field of fractions).
- * `FractionalIdeal R⁰ K` is the type of fractional ideals in the field of fractions
- * `Div (FractionalIdeal R⁰ K)` instance:
-   the ideal quotient `I / J` (typically written $I : J$, but a `:` operator cannot be defined)
 
 ## Main statements
 
   * `mul_left_mono` and `mul_right_mono` state that ideal multiplication is monotone
   * `mul_div_self_cancel_iff` states that `1 / I` is the inverse of `I` if one exists
-  * `isNoetherian` states that every fractional ideal of a noetherian integral domain is noetherian
 
 ## Implementation notes
 
@@ -69,11 +56,7 @@ fractional ideal, fractional ideals, invertible ideal
 -/
 
 
-open IsLocalization
-
-open Pointwise
-
-open nonZeroDivisors
+open IsLocalization Pointwise nonZeroDivisors
 
 section Defs
 
@@ -104,9 +87,7 @@ end Defs
 
 namespace FractionalIdeal
 
-open Set
-
-open Submodule
+open Set Submodule
 
 variable {R : Type*} [CommRing R] {S : Submonoid R} {P : Type*} [CommRing P]
 
@@ -663,6 +644,8 @@ instance commSemiring : CommSemiring (FractionalIdeal S P) :=
   Function.Injective.commSemiring _ Subtype.coe_injective coe_zero coe_one coe_add coe_mul
     (fun _ _ => coe_nsmul _ _) coe_pow coe_nat_cast
 
+end Semiring
+
 variable (S P)
 
 /-- `FractionalIdeal.coeToSubmodule` as a bundled `RingHom`. -/
@@ -760,932 +743,4 @@ theorem coeIdeal_finprod [IsLocalization S P] {α : Sort*} {f : α → Ideal R}
 
 end Order
 
-variable {P' : Type*} [CommRing P'] [Algebra R P'] [loc' : IsLocalization S P']
-
-variable {P'' : Type*} [CommRing P''] [Algebra R P''] [loc'' : IsLocalization S P'']
-
-theorem _root_.IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
-    IsFractional S I → IsFractional S (Submodule.map g.toLinearMap I)
-  | ⟨a, a_nonzero, hI⟩ =>
-    ⟨a, a_nonzero, fun b hb => by
-      obtain ⟨b', b'_mem, hb'⟩ := Submodule.mem_map.mp hb
-      rw [AlgHom.toLinearMap_apply] at hb'
-      obtain ⟨x, hx⟩ := hI b' b'_mem
-      use x
-      rw [← g.commutes, hx, g.map_smul, hb']⟩
-#align is_fractional.map IsFractional.map
-
-/-- `I.map g` is the pushforward of the fractional ideal `I` along the algebra morphism `g` -/
-def map (g : P →ₐ[R] P') : FractionalIdeal S P → FractionalIdeal S P' := fun I =>
-  ⟨Submodule.map g.toLinearMap I, I.isFractional.map g⟩
-#align fractional_ideal.map FractionalIdeal.map
-
-@[simp, norm_cast]
-theorem coe_map (g : P →ₐ[R] P') (I : FractionalIdeal S P) :
-    ↑(map g I) = Submodule.map g.toLinearMap I :=
-  rfl
-#align fractional_ideal.coe_map FractionalIdeal.coe_map
-
-@[simp]
-theorem mem_map {I : FractionalIdeal S P} {g : P →ₐ[R] P'} {y : P'} :
-    y ∈ I.map g ↔ ∃ x, x ∈ I ∧ g x = y :=
-  Submodule.mem_map
-#align fractional_ideal.mem_map FractionalIdeal.mem_map
-
-variable (I J : FractionalIdeal S P) (g : P →ₐ[R] P')
-
-@[simp]
-theorem map_id : I.map (AlgHom.id _ _) = I :=
-  coeToSubmodule_injective (Submodule.map_id (I : Submodule R P))
-#align fractional_ideal.map_id FractionalIdeal.map_id
-
-@[simp]
-theorem map_comp (g' : P' →ₐ[R] P'') : I.map (g'.comp g) = (I.map g).map g' :=
-  coeToSubmodule_injective (Submodule.map_comp g.toLinearMap g'.toLinearMap I)
-#align fractional_ideal.map_comp FractionalIdeal.map_comp
-
-@[simp, norm_cast]
-theorem map_coeIdeal (I : Ideal R) : (I : FractionalIdeal S P).map g = I := by
-  ext x
-  simp only [mem_coeIdeal]
-  constructor
-  · rintro ⟨_, ⟨y, hy, rfl⟩, rfl⟩
-    exact ⟨y, hy, (g.commutes y).symm⟩
-  · rintro ⟨y, hy, rfl⟩
-    exact ⟨_, ⟨y, hy, rfl⟩, g.commutes y⟩
-#align fractional_ideal.map_coe_ideal FractionalIdeal.map_coeIdeal
-
-@[simp]
-theorem map_one : (1 : FractionalIdeal S P).map g = 1 :=
-  map_coeIdeal g ⊤
-#align fractional_ideal.map_one FractionalIdeal.map_one
-
-@[simp]
-theorem map_zero : (0 : FractionalIdeal S P).map g = 0 :=
-  map_coeIdeal g 0
-#align fractional_ideal.map_zero FractionalIdeal.map_zero
-
-@[simp]
-theorem map_add : (I + J).map g = I.map g + J.map g :=
-  coeToSubmodule_injective (Submodule.map_sup _ _ _)
-#align fractional_ideal.map_add FractionalIdeal.map_add
-
-@[simp]
-theorem map_mul : (I * J).map g = I.map g * J.map g := by
-  simp only [mul_def]
-  exact coeToSubmodule_injective (Submodule.map_mul _ _ _)
-#align fractional_ideal.map_mul FractionalIdeal.map_mul
-
-@[simp]
-theorem map_map_symm (g : P ≃ₐ[R] P') : (I.map (g : P →ₐ[R] P')).map (g.symm : P' →ₐ[R] P) = I := by
-  rw [← map_comp, g.symm_comp, map_id]
-#align fractional_ideal.map_map_symm FractionalIdeal.map_map_symm
-
-@[simp]
-theorem map_symm_map (I : FractionalIdeal S P') (g : P ≃ₐ[R] P') :
-    (I.map (g.symm : P' →ₐ[R] P)).map (g : P →ₐ[R] P') = I := by
-  rw [← map_comp, g.comp_symm, map_id]
-#align fractional_ideal.map_symm_map FractionalIdeal.map_symm_map
-
-theorem map_mem_map {f : P →ₐ[R] P'} (h : Function.Injective f) {x : P} {I : FractionalIdeal S P} :
-    f x ∈ map f I ↔ x ∈ I :=
-  mem_map.trans ⟨fun ⟨_, hx', x'_eq⟩ => h x'_eq ▸ hx', fun h => ⟨x, h, rfl⟩⟩
-#align fractional_ideal.map_mem_map FractionalIdeal.map_mem_map
-
-theorem map_injective (f : P →ₐ[R] P') (h : Function.Injective f) :
-    Function.Injective (map f : FractionalIdeal S P → FractionalIdeal S P') := fun _ _ hIJ =>
-  ext fun _ => (map_mem_map h).symm.trans (hIJ.symm ▸ map_mem_map h)
-#align fractional_ideal.map_injective FractionalIdeal.map_injective
-
-/-- If `g` is an equivalence, `map g` is an isomorphism -/
-def mapEquiv (g : P ≃ₐ[R] P') : FractionalIdeal S P ≃+* FractionalIdeal S P' where
-  toFun := map g
-  invFun := map g.symm
-  map_add' I J := map_add I J _
-  map_mul' I J := map_mul I J _
-  left_inv I := by rw [← map_comp, AlgEquiv.symm_comp, map_id]
-  right_inv I := by rw [← map_comp, AlgEquiv.comp_symm, map_id]
-#align fractional_ideal.map_equiv FractionalIdeal.mapEquiv
-
-@[simp]
-theorem coeFun_mapEquiv (g : P ≃ₐ[R] P') :
-    (mapEquiv g : FractionalIdeal S P → FractionalIdeal S P') = map g :=
-  rfl
-#align fractional_ideal.coe_fun_map_equiv FractionalIdeal.coeFun_mapEquiv
-
-@[simp]
-theorem mapEquiv_apply (g : P ≃ₐ[R] P') (I : FractionalIdeal S P) : mapEquiv g I = map (↑g) I :=
-  rfl
-#align fractional_ideal.map_equiv_apply FractionalIdeal.mapEquiv_apply
-
-@[simp]
-theorem mapEquiv_symm (g : P ≃ₐ[R] P') :
-    ((mapEquiv g).symm : FractionalIdeal S P' ≃+* _) = mapEquiv g.symm :=
-  rfl
-#align fractional_ideal.map_equiv_symm FractionalIdeal.mapEquiv_symm
-
-@[simp]
-theorem mapEquiv_refl : mapEquiv AlgEquiv.refl = RingEquiv.refl (FractionalIdeal S P) :=
-  RingEquiv.ext fun x => by simp
-#align fractional_ideal.map_equiv_refl FractionalIdeal.mapEquiv_refl
-
-theorem isFractional_span_iff {s : Set P} :
-    IsFractional S (span R s) ↔ ∃ a ∈ S, ∀ b : P, b ∈ s → IsInteger R (a • b) :=
-  ⟨fun ⟨a, a_mem, h⟩ => ⟨a, a_mem, fun b hb => h b (subset_span hb)⟩, fun ⟨a, a_mem, h⟩ =>
-    ⟨a, a_mem, fun b hb =>
-      span_induction hb h
-        (by
-          rw [smul_zero]
-          exact isInteger_zero)
-        (fun x y hx hy => by
-          rw [smul_add]
-          exact isInteger_add hx hy)
-        fun s x hx => by
-        rw [smul_comm]
-        exact isInteger_smul hx⟩⟩
-#align fractional_ideal.is_fractional_span_iff FractionalIdeal.isFractional_span_iff
-
-theorem isFractional_of_fg {I : Submodule R P} (hI : I.FG) : IsFractional S I := by
-  rcases hI with ⟨I, rfl⟩
-  rcases exist_integer_multiples_of_finset S I with ⟨⟨s, hs1⟩, hs⟩
-  rw [isFractional_span_iff]
-  exact ⟨s, hs1, hs⟩
-#align fractional_ideal.is_fractional_of_fg FractionalIdeal.isFractional_of_fg
-
-theorem mem_span_mul_finite_of_mem_mul {I J : FractionalIdeal S P} {x : P} (hx : x ∈ I * J) :
-    ∃ T T' : Finset P, (T : Set P) ⊆ I ∧ (T' : Set P) ⊆ J ∧ x ∈ span R (T * T' : Set P) :=
-  Submodule.mem_span_mul_finite_of_mem_mul (by simpa using mem_coe.mpr hx)
-#align fractional_ideal.mem_span_mul_finite_of_mem_mul FractionalIdeal.mem_span_mul_finite_of_mem_mul
-
-variable (S)
-
-theorem coeIdeal_fg (inj : Function.Injective (algebraMap R P)) (I : Ideal R) :
-    FG ((I : FractionalIdeal S P) : Submodule R P) ↔ I.FG :=
-  coeSubmodule_fg _ inj _
-#align fractional_ideal.coe_ideal_fg FractionalIdeal.coeIdeal_fg
-
-variable {S}
-
-theorem fg_unit (I : (FractionalIdeal S P)ˣ) : FG (I : Submodule R P) :=
-  Submodule.fg_unit <| Units.map (coeSubmoduleHom S P).toMonoidHom I
-#align fractional_ideal.fg_unit FractionalIdeal.fg_unit
-
-theorem fg_of_isUnit (I : FractionalIdeal S P) (h : IsUnit I) : FG (I : Submodule R P) :=
-  fg_unit h.unit
-#align fractional_ideal.fg_of_is_unit FractionalIdeal.fg_of_isUnit
-
-theorem _root_.Ideal.fg_of_isUnit (inj : Function.Injective (algebraMap R P)) (I : Ideal R)
-    (h : IsUnit (I : FractionalIdeal S P)) : I.FG := by
-  rw [← coeIdeal_fg S inj I]
-  exact FractionalIdeal.fg_of_isUnit I h
-#align ideal.fg_of_is_unit Ideal.fg_of_isUnit
-
-variable (S P P')
-
-/-- `canonicalEquiv f f'` is the canonical equivalence between the fractional
-ideals in `P` and in `P'`, which are both localizations of `R` at `S`. -/
-noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* FractionalIdeal S P' :=
-  mapEquiv
-    { ringEquivOfRingEquiv P P' (RingEquiv.refl R)
-        (show S.map _ = S by rw [RingEquiv.toMonoidHom_refl, Submonoid.map_id]) with
-      commutes' := fun r => ringEquivOfRingEquiv_eq _ _ }
-#align fractional_ideal.canonical_equiv FractionalIdeal.canonicalEquiv
-
-@[simp]
-theorem mem_canonicalEquiv_apply {I : FractionalIdeal S P} {x : P'} :
-    x ∈ canonicalEquiv S P P' I ↔
-      ∃ y ∈ I,
-        IsLocalization.map P' (RingHom.id R) (fun y (hy : y ∈ S) => show RingHom.id R y ∈ S from hy)
-            (y : P) =
-          x := by
-  rw [canonicalEquiv, mapEquiv_apply, mem_map]
-  exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
-#align fractional_ideal.mem_canonical_equiv_apply FractionalIdeal.mem_canonicalEquiv_apply
-
-@[simp]
-theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P' P :=
-  RingEquiv.ext fun I =>
-    SetLike.ext_iff.mpr fun x => by
-      rw [mem_canonicalEquiv_apply, canonicalEquiv, mapEquiv_symm, mapEquiv_apply,
-        mem_map]
-      exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩
-#align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symm
-
-theorem canonicalEquiv_flip (I) : canonicalEquiv S P P' (canonicalEquiv S P' P I) = I := by
-  rw [← canonicalEquiv_symm]; erw [RingEquiv.apply_symm_apply]
-#align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flip
-
-@[simp]
-theorem canonicalEquiv_canonicalEquiv (P'' : Type*) [CommRing P''] [Algebra R P'']
-    [IsLocalization S P''] (I : FractionalIdeal S P) :
-    canonicalEquiv S P' P'' (canonicalEquiv S P P' I) = canonicalEquiv S P P'' I := by
-  ext
-  simp only [IsLocalization.map_map, RingHomInvPair.comp_eq₂, mem_canonicalEquiv_apply,
-    exists_prop, exists_exists_and_eq_and]
-#align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquiv
-
-theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type*) [CommRing P''] [Algebra R P'']
-    [IsLocalization S P''] :
-    (canonicalEquiv S P P').trans (canonicalEquiv S P' P'') = canonicalEquiv S P P'' :=
-  RingEquiv.ext (canonicalEquiv_canonicalEquiv S P P' P'')
-#align fractional_ideal.canonical_equiv_trans_canonical_equiv FractionalIdeal.canonicalEquiv_trans_canonicalEquiv
-
-@[simp]
-theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I := by
-  ext
-  simp [IsLocalization.map_eq]
-#align fractional_ideal.canonical_equiv_coe_ideal FractionalIdeal.canonicalEquiv_coeIdeal
-
-@[simp]
-theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ := by
-  rw [← canonicalEquiv_trans_canonicalEquiv S P P]
-  convert (canonicalEquiv S P P).symm_trans_self
-  exact (canonicalEquiv_symm S P P).symm
-#align fractional_ideal.canonical_equiv_self FractionalIdeal.canonicalEquiv_self
-
-end Semiring
-
-section IsFractionRing
-
-/-!
-### `IsFractionRing` section
-
-This section concerns fractional ideals in the field of fractions,
-i.e. the type `FractionalIdeal R⁰ K` where `IsFractionRing R K`.
--/
-
-
-variable {K K' : Type*} [Field K] [Field K']
-
-variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
-
-variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
-
-/-- Nonzero fractional ideals contain a nonzero integer. -/
-theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
-    ∃ x, x ≠ 0 ∧ algebraMap R K x ∈ I := by
-  obtain ⟨y : K, y_mem, y_not_mem⟩ :=
-    SetLike.exists_of_lt (by simpa only using bot_lt_iff_ne_bot.mpr hI)
-  have y_ne_zero : y ≠ 0 := by simpa using y_not_mem
-  obtain ⟨z, ⟨x, hx⟩⟩ := exists_integer_multiple R⁰ y
-  refine' ⟨x, _, _⟩
-  · rw [Ne.def, ← @IsFractionRing.to_map_eq_zero_iff R _ K, hx, Algebra.smul_def]
-    exact mul_ne_zero (IsFractionRing.to_map_ne_zero_of_mem_nonZeroDivisors z.2) y_ne_zero
-  · rw [hx]
-    exact smul_mem _ _ y_mem
-#align fractional_ideal.exists_ne_zero_mem_is_integer FractionalIdeal.exists_ne_zero_mem_isInteger
-
-theorem map_ne_zero [Nontrivial R] (hI : I ≠ 0) : I.map h ≠ 0 := by
-  obtain ⟨x, x_ne_zero, hx⟩ := exists_ne_zero_mem_isInteger hI
-  contrapose! x_ne_zero with map_eq_zero
-  refine' IsFractionRing.to_map_eq_zero_iff.mp (eq_zero_iff.mp map_eq_zero _ (mem_map.mpr _))
-  exact ⟨algebraMap R K x, hx, h.commutes x⟩
-#align fractional_ideal.map_ne_zero FractionalIdeal.map_ne_zero
-
-@[simp]
-theorem map_eq_zero_iff [Nontrivial R] : I.map h = 0 ↔ I = 0 :=
-  ⟨not_imp_not.mp (map_ne_zero _), fun hI => hI.symm ▸ map_zero h⟩
-#align fractional_ideal.map_eq_zero_iff FractionalIdeal.map_eq_zero_iff
-
-theorem coeIdeal_injective : Function.Injective (fun (I : Ideal R) ↦ (I : FractionalIdeal R⁰ K)) :=
-  coeIdeal_injective' le_rfl
-#align fractional_ideal.coe_ideal_injective FractionalIdeal.coeIdeal_injective
-
-theorem coeIdeal_inj {I J : Ideal R} :
-    (I : FractionalIdeal R⁰ K) = (J : FractionalIdeal R⁰ K) ↔ I = J :=
-  coeIdeal_inj' le_rfl
-#align fractional_ideal.coe_ideal_inj FractionalIdeal.coeIdeal_inj
-
-@[simp]
-theorem coeIdeal_eq_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 0 ↔ I = ⊥ :=
-  coeIdeal_eq_zero' le_rfl
-#align fractional_ideal.coe_ideal_eq_zero FractionalIdeal.coeIdeal_eq_zero
-
-theorem coeIdeal_ne_zero {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 0 ↔ I ≠ ⊥ :=
-  coeIdeal_ne_zero' le_rfl
-#align fractional_ideal.coe_ideal_ne_zero FractionalIdeal.coeIdeal_ne_zero
-
-@[simp]
-theorem coeIdeal_eq_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) = 1 ↔ I = 1 := by
-  simpa only [Ideal.one_eq_top] using coeIdeal_inj
-#align fractional_ideal.coe_ideal_eq_one FractionalIdeal.coeIdeal_eq_one
-
-theorem coeIdeal_ne_one {I : Ideal R} : (I : FractionalIdeal R⁰ K) ≠ 1 ↔ I ≠ 1 :=
-  not_iff_not.mpr coeIdeal_eq_one
-#align fractional_ideal.coe_ideal_ne_one FractionalIdeal.coeIdeal_ne_one
-
-end IsFractionRing
-
-section Quotient
-
-/-!
-### `quotient` section
-
-This section defines the ideal quotient of fractional ideals.
-
-In this section we need that each non-zero `y : R` has an inverse in
-the localization, i.e. that the localization is a field. We satisfy this
-assumption by taking `S = nonZeroDivisors R`, `R`'s localization at which
-is a field because `R` is a domain.
--/
-
-
-open Classical
-
-variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
-
-variable [Algebra R₁ K] [frac : IsFractionRing R₁ K]
-
-instance : Nontrivial (FractionalIdeal R₁⁰ K) :=
-  ⟨⟨0, 1, fun h =>
-      have this : (1 : K) ∈ (0 : FractionalIdeal R₁⁰ K) := by
-        rw [← (algebraMap R₁ K).map_one]
-        simpa only [h] using coe_mem_one R₁⁰ 1
-      one_ne_zero ((mem_zero_iff _).mp this)⟩⟩
-
-theorem ne_zero_of_mul_eq_one (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) : I ≠ 0 := fun hI =>
-  zero_ne_one' (FractionalIdeal R₁⁰ K)
-    (by
-      convert h
-      simp [hI])
-#align fractional_ideal.ne_zero_of_mul_eq_one FractionalIdeal.ne_zero_of_mul_eq_one
-
-variable [IsDomain R₁]
-
-theorem _root_.IsFractional.div_of_nonzero {I J : Submodule R₁ K} :
-    IsFractional R₁⁰ I → IsFractional R₁⁰ J → J ≠ 0 → IsFractional R₁⁰ (I / J)
-  | ⟨aI, haI, hI⟩, ⟨aJ, haJ, hJ⟩, h => by
-    obtain ⟨y, mem_J, not_mem_zero⟩ :=
-      SetLike.exists_of_lt (show 0 < J by simpa only using bot_lt_iff_ne_bot.mpr h)
-    obtain ⟨y', hy'⟩ := hJ y mem_J
-    use aI * y'
-    constructor
-    · apply (nonZeroDivisors R₁).mul_mem haI (mem_nonZeroDivisors_iff_ne_zero.mpr _)
-      intro y'_eq_zero
-      have : algebraMap R₁ K aJ * y = 0 := by
-        rw [← Algebra.smul_def, ← hy', y'_eq_zero, RingHom.map_zero]
-      have y_zero :=
-        (mul_eq_zero.mp this).resolve_left
-          (mt ((injective_iff_map_eq_zero (algebraMap R₁ K)).1 (IsFractionRing.injective _ _) _)
-            (mem_nonZeroDivisors_iff_ne_zero.mp haJ))
-      apply not_mem_zero
-      simpa
-    intro b hb
-    convert hI _ (hb _ (Submodule.smul_mem _ aJ mem_J)) using 1
-    rw [← hy', mul_comm b, ← Algebra.smul_def, mul_smul]
-#align is_fractional.div_of_nonzero IsFractional.div_of_nonzero
-
-theorem fractional_div_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
-    IsFractional R₁⁰ (I / J : Submodule R₁ K) :=
-  I.isFractional.div_of_nonzero J.isFractional fun H =>
-    h <| coeToSubmodule_injective <| H.trans coe_zero.symm
-#align fractional_ideal.fractional_div_of_nonzero FractionalIdeal.fractional_div_of_nonzero
-
-noncomputable instance : Div (FractionalIdeal R₁⁰ K) :=
-  ⟨fun I J => if h : J = 0 then 0 else ⟨I / J, fractional_div_of_nonzero h⟩⟩
-
-variable {I J : FractionalIdeal R₁⁰ K}
-
-@[simp]
-theorem div_zero {I : FractionalIdeal R₁⁰ K} : I / 0 = 0 :=
-  dif_pos rfl
-#align fractional_ideal.div_zero FractionalIdeal.div_zero
-
-theorem div_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) :
-    I / J = ⟨I / J, fractional_div_of_nonzero h⟩ :=
-  dif_neg h
-#align fractional_ideal.div_nonzero FractionalIdeal.div_nonzero
-
-@[simp]
-theorem coe_div {I J : FractionalIdeal R₁⁰ K} (hJ : J ≠ 0) :
-    (↑(I / J) : Submodule R₁ K) = ↑I / (↑J : Submodule R₁ K) :=
-  congr_arg _ (dif_neg hJ)
-#align fractional_ideal.coe_div FractionalIdeal.coe_div
-
-theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {x} :
-    x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I := by
-  rw [div_nonzero h]
-  exact Submodule.mem_div_iff_forall_mul_mem
-#align fractional_ideal.mem_div_iff_of_nonzero FractionalIdeal.mem_div_iff_of_nonzero
-
-theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 := by
-  by_cases hI : I = 0
-  · rw [hI, div_zero, mul_zero]
-    exact zero_le 1
-  · rw [← coe_le_coe, coe_mul, coe_div hI, coe_one]
-    apply Submodule.mul_one_div_le_one
-#align fractional_ideal.mul_one_div_le_one FractionalIdeal.mul_one_div_le_one
-
-theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
-    I ≤ I * (1 / I) := by
-  by_cases hI_nz : I = 0
-  · rw [hI_nz, div_zero, mul_zero]
-  · rw [← coe_le_coe, coe_mul, coe_div hI_nz, coe_one]
-    rw [← coe_le_coe, coe_one] at hI
-    exact Submodule.le_self_mul_one_div hI
-#align fractional_ideal.le_self_mul_one_div FractionalIdeal.le_self_mul_one_div
-
-theorem le_div_iff_of_nonzero {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
-    I ≤ J / J' ↔ ∀ x ∈ I, ∀ y ∈ J', x * y ∈ J :=
-  ⟨fun h _ hx => (mem_div_iff_of_nonzero hJ').mp (h hx), fun h x hx =>
-    (mem_div_iff_of_nonzero hJ').mpr (h x hx)⟩
-#align fractional_ideal.le_div_iff_of_nonzero FractionalIdeal.le_div_iff_of_nonzero
-
-theorem le_div_iff_mul_le {I J J' : FractionalIdeal R₁⁰ K} (hJ' : J' ≠ 0) :
-    I ≤ J / J' ↔ I * J' ≤ J := by
-  rw [div_nonzero hJ']
-  -- Porting note: this used to be { convert; rw }, flipped the order.
-  rw [← coe_le_coe (I := I * J') (J := J), coe_mul]
-  exact Submodule.le_div_iff_mul_le
-#align fractional_ideal.le_div_iff_mul_le FractionalIdeal.le_div_iff_mul_le
-
-@[simp]
-theorem div_one {I : FractionalIdeal R₁⁰ K} : I / 1 = I := by
-  rw [div_nonzero (one_ne_zero' (FractionalIdeal R₁⁰ K))]
-  ext
-  constructor <;> intro h
-  · simpa using mem_div_iff_forall_mul_mem.mp h 1 ((algebraMap R₁ K).map_one ▸ coe_mem_one R₁⁰ 1)
-  · apply mem_div_iff_forall_mul_mem.mpr
-    rintro y ⟨y', _, rfl⟩
-    -- Porting note: this used to be { convert; rw }, flipped the order.
-    rw [mul_comm, Algebra.linearMap_apply, ← Algebra.smul_def]
-    exact Submodule.smul_mem _ y' h
-#align fractional_ideal.div_one FractionalIdeal.div_one
-
-theorem eq_one_div_of_mul_eq_one_right (I J : FractionalIdeal R₁⁰ K) (h : I * J = 1) :
-    J = 1 / I := by
-  have hI : I ≠ 0 := ne_zero_of_mul_eq_one I J h
-  suffices h' : I * (1 / I) = 1
-  · exact
-      congr_arg Units.inv <|
-        @Units.ext _ _ (Units.mkOfMulEqOne _ _ h) (Units.mkOfMulEqOne _ _ h') rfl
-  apply le_antisymm
-  · apply mul_le.mpr _
-    intro x hx y hy
-    rw [mul_comm]
-    exact (mem_div_iff_of_nonzero hI).mp hy x hx
-  rw [← h]
-  apply mul_left_mono I
-  apply (le_div_iff_of_nonzero hI).mpr _
-  intro y hy x hx
-  rw [mul_comm]
-  exact mul_mem_mul hx hy
-#align fractional_ideal.eq_one_div_of_mul_eq_one_right FractionalIdeal.eq_one_div_of_mul_eq_one_right
-
-theorem mul_div_self_cancel_iff {I : FractionalIdeal R₁⁰ K} : I * (1 / I) = 1 ↔ ∃ J, I * J = 1 :=
-  ⟨fun h => ⟨1 / I, h⟩, fun ⟨J, hJ⟩ => by rwa [← eq_one_div_of_mul_eq_one_right I J hJ]⟩
-#align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iff
-
-variable {K' : Type*} [Field K'] [Algebra R₁ K'] [IsFractionRing R₁ K']
-
-@[simp]
-theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
-    (I / J).map (h : K →ₐ[R₁] K') = I.map h / J.map h := by
-  by_cases H : J = 0
-  · rw [H, div_zero, map_zero, div_zero]
-  · -- Porting note: `simp` wouldn't apply these lemmas so do them manually using `rw`
-    rw [← coeToSubmodule_inj, div_nonzero H, div_nonzero (map_ne_zero _ H)]
-    simp [Submodule.map_div]
-#align fractional_ideal.map_div FractionalIdeal.map_div
-
--- Porting note: doesn't need to be @[simp] because this follows from `map_one` and `map_div`
-theorem map_one_div (I : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
-    (1 / I).map (h : K →ₐ[R₁] K') = 1 / I.map h := by rw [map_div, map_one]
-#align fractional_ideal.map_one_div FractionalIdeal.map_one_div
-
-end Quotient
-
-section Field
-
-variable {R₁ K L : Type*} [CommRing R₁] [Field K] [Field L]
-
-variable [Algebra R₁ K] [IsFractionRing R₁ K] [Algebra K L] [IsFractionRing K L]
-
-theorem eq_zero_or_one (I : FractionalIdeal K⁰ L) : I = 0 ∨ I = 1 := by
-  rw [or_iff_not_imp_left]
-  intro hI
-  simp_rw [@SetLike.ext_iff _ _ _ I 1, mem_one_iff]
-  intro x
-  constructor
-  · intro x_mem
-    obtain ⟨n, d, rfl⟩ := IsLocalization.mk'_surjective K⁰ x
-    refine' ⟨n / d, _⟩
-    rw [map_div₀, IsFractionRing.mk'_eq_div]
-  · rintro ⟨x, rfl⟩
-    obtain ⟨y, y_ne, y_mem⟩ := exists_ne_zero_mem_isInteger hI
-    rw [← div_mul_cancel x y_ne, RingHom.map_mul, ← Algebra.smul_def]
-    exact smul_mem (M := L) I (x / y) y_mem
-#align fractional_ideal.eq_zero_or_one FractionalIdeal.eq_zero_or_one
-
-theorem eq_zero_or_one_of_isField (hF : IsField R₁) (I : FractionalIdeal R₁⁰ K) : I = 0 ∨ I = 1 :=
-  letI : Field R₁ := hF.toField
-  eq_zero_or_one I
-#align fractional_ideal.eq_zero_or_one_of_is_field FractionalIdeal.eq_zero_or_one_of_isField
-
-end Field
-
-section PrincipalIdealRing
-
-variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
-
-variable [Algebra R₁ K] [IsFractionRing R₁ K]
-
-open Classical
-
-variable (R₁)
-
-/-- `FractionalIdeal.span_finset R₁ s f` is the fractional ideal of `R₁` generated by `f '' s`. -/
--- Porting note: `@[simps]` generated a `Subtype.val` coercion instead of a
--- `FractionalIdeal.coeToSubmodule` coercion
-def spanFinset {ι : Type*} (s : Finset ι) (f : ι → K) : FractionalIdeal R₁⁰ K :=
-  ⟨Submodule.span R₁ (f '' s), by
-    obtain ⟨a', ha'⟩ := IsLocalization.exist_integer_multiples R₁⁰ s f
-    refine' ⟨a', a'.2, fun x hx => Submodule.span_induction hx _ _ _ _⟩
-    · rintro _ ⟨i, hi, rfl⟩
-      exact ha' i hi
-    · rw [smul_zero]
-      exact IsLocalization.isInteger_zero
-    · intro x y hx hy
-      rw [smul_add]
-      exact IsLocalization.isInteger_add hx hy
-    · intro c x hx
-      rw [smul_comm]
-      exact IsLocalization.isInteger_smul hx⟩
-#align fractional_ideal.span_finset FractionalIdeal.spanFinset
-
-@[simp] lemma spanFinset_coe {ι : Type*} (s : Finset ι) (f : ι → K) :
-    (spanFinset R₁ s f : Submodule R₁ K) = Submodule.span R₁ (f '' s) :=
-  rfl
-
-variable {R₁}
-
-@[simp]
-theorem spanFinset_eq_zero {ι : Type*} {s : Finset ι} {f : ι → K} :
-    spanFinset R₁ s f = 0 ↔ ∀ j ∈ s, f j = 0 := by
-  simp only [← coeToSubmodule_inj, spanFinset_coe, coe_zero, Submodule.span_eq_bot,
-    Set.mem_image, Finset.mem_coe, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
-#align fractional_ideal.span_finset_eq_zero FractionalIdeal.spanFinset_eq_zero
-
-theorem spanFinset_ne_zero {ι : Type*} {s : Finset ι} {f : ι → K} :
-    spanFinset R₁ s f ≠ 0 ↔ ∃ j ∈ s, f j ≠ 0 := by simp
-#align fractional_ideal.span_finset_ne_zero FractionalIdeal.spanFinset_ne_zero
-
-open Submodule.IsPrincipal
-
-theorem isFractional_span_singleton (x : P) : IsFractional S (span R {x} : Submodule R P) :=
-  let ⟨a, ha⟩ := exists_integer_multiple S x
-  isFractional_span_iff.mpr ⟨a, a.2, fun _ hx' => (Set.mem_singleton_iff.mp hx').symm ▸ ha⟩
-#align fractional_ideal.is_fractional_span_singleton FractionalIdeal.isFractional_span_singleton
-
-variable (S)
-
-/-- `spanSingleton x` is the fractional ideal generated by `x` if `0 ∉ S` -/
-irreducible_def spanSingleton (x : P) : FractionalIdeal S P :=
-  ⟨span R {x}, isFractional_span_singleton x⟩
-#align fractional_ideal.span_singleton FractionalIdeal.spanSingleton
-
--- local attribute [semireducible] span_singleton
-@[simp]
-theorem coe_spanSingleton (x : P) : (spanSingleton S x : Submodule R P) = span R {x} := by
-  rw [spanSingleton]
-  rfl
-#align fractional_ideal.coe_span_singleton FractionalIdeal.coe_spanSingleton
-
-@[simp]
-theorem mem_spanSingleton {x y : P} : x ∈ spanSingleton S y ↔ ∃ z : R, z • y = x := by
-  rw [spanSingleton]
-  exact Submodule.mem_span_singleton
-#align fractional_ideal.mem_span_singleton FractionalIdeal.mem_spanSingleton
-
-theorem mem_spanSingleton_self (x : P) : x ∈ spanSingleton S x :=
-  (mem_spanSingleton S).mpr ⟨1, one_smul _ _⟩
-#align fractional_ideal.mem_span_singleton_self FractionalIdeal.mem_spanSingleton_self
-
-/-- A version of `FractionalIdeal.den_mul_self_eq_num` in terms of fractional ideals. -/
-theorem den_mul_self_eq_num' (I : FractionalIdeal S P) :
-    spanSingleton S (algebraMap R P I.den) * I = I.num := by
-  apply coeToSubmodule_injective
-  dsimp only
-  rw [coe_mul, ← smul_eq_mul, coe_spanSingleton, smul_eq_mul, Submodule.span_singleton_mul]
-  convert I.den_mul_self_eq_num using 1
-  ext
-  erw [Set.mem_smul_set, Set.mem_smul_set]
-  simp [Algebra.smul_def]
-
-variable {S}
-
-@[simp]
-theorem spanSingleton_le_iff_mem {x : P} {I : FractionalIdeal S P} :
-    spanSingleton S x ≤ I ↔ x ∈ I := by
-  rw [← coe_le_coe, coe_spanSingleton, Submodule.span_singleton_le_iff_mem, mem_coe]
-#align fractional_ideal.span_singleton_le_iff_mem FractionalIdeal.spanSingleton_le_iff_mem
-
-theorem spanSingleton_eq_spanSingleton [NoZeroSMulDivisors R P] {x y : P} :
-    spanSingleton S x = spanSingleton S y ↔ ∃ z : Rˣ, z • x = y := by
-  rw [← Submodule.span_singleton_eq_span_singleton, spanSingleton, spanSingleton]
-  exact Subtype.mk_eq_mk
-#align fractional_ideal.span_singleton_eq_span_singleton FractionalIdeal.spanSingleton_eq_spanSingleton
-
-theorem eq_spanSingleton_of_principal (I : FractionalIdeal S P) [IsPrincipal (I : Submodule R P)] :
-    I = spanSingleton S (generator (I : Submodule R P)) := by
-  -- Porting note: this used to be `coeToSubmodule_injective (span_singleton_generator ↑I).symm`
-  -- but Lean 4 struggled to unify everything. Turned it into an explicit `rw`.
-  rw [spanSingleton, ← coeToSubmodule_inj, coe_mk, span_singleton_generator]
-#align fractional_ideal.eq_span_singleton_of_principal FractionalIdeal.eq_spanSingleton_of_principal
-
-theorem isPrincipal_iff (I : FractionalIdeal S P) :
-    IsPrincipal (I : Submodule R P) ↔ ∃ x, I = spanSingleton S x :=
-  ⟨fun h => ⟨@generator _ _ _ _ _ (↑I) h, @eq_spanSingleton_of_principal _ _ _ _ _ _ _ I h⟩,
-    fun ⟨x, hx⟩ => { principal' := ⟨x, Eq.trans (congr_arg _ hx) (coe_spanSingleton _ x)⟩ }⟩
-#align fractional_ideal.is_principal_iff FractionalIdeal.isPrincipal_iff
-
-@[simp]
-theorem spanSingleton_zero : spanSingleton S (0 : P) = 0 := by
-  ext
-  simp [Submodule.mem_span_singleton, eq_comm]
-#align fractional_ideal.span_singleton_zero FractionalIdeal.spanSingleton_zero
-
-theorem spanSingleton_eq_zero_iff {y : P} : spanSingleton S y = 0 ↔ y = 0 :=
-  ⟨fun h =>
-    span_eq_bot.mp (by simpa using congr_arg Subtype.val h : span R {y} = ⊥) y (mem_singleton y),
-    fun h => by simp [h]⟩
-#align fractional_ideal.span_singleton_eq_zero_iff FractionalIdeal.spanSingleton_eq_zero_iff
-
-theorem spanSingleton_ne_zero_iff {y : P} : spanSingleton S y ≠ 0 ↔ y ≠ 0 :=
-  not_congr spanSingleton_eq_zero_iff
-#align fractional_ideal.span_singleton_ne_zero_iff FractionalIdeal.spanSingleton_ne_zero_iff
-
-@[simp]
-theorem spanSingleton_one : spanSingleton S (1 : P) = 1 := by
-  ext
-  refine' (mem_spanSingleton S).trans ((exists_congr _).trans (mem_one_iff S).symm)
-  intro x'
-  rw [Algebra.smul_def, mul_one]
-#align fractional_ideal.span_singleton_one FractionalIdeal.spanSingleton_one
-
-@[simp]
-theorem spanSingleton_mul_spanSingleton (x y : P) :
-    spanSingleton S x * spanSingleton S y = spanSingleton S (x * y) := by
-  apply coeToSubmodule_injective
-  simp only [coe_mul, coe_spanSingleton, span_mul_span, singleton_mul_singleton]
-#align fractional_ideal.span_singleton_mul_span_singleton FractionalIdeal.spanSingleton_mul_spanSingleton
-
-@[simp]
-theorem spanSingleton_pow (x : P) (n : ℕ) : spanSingleton S x ^ n = spanSingleton S (x ^ n) := by
-  induction' n with n hn
-  · rw [pow_zero, pow_zero, spanSingleton_one]
-  · rw [pow_succ, hn, spanSingleton_mul_spanSingleton, pow_succ]
-#align fractional_ideal.span_singleton_pow FractionalIdeal.spanSingleton_pow
-
-@[simp]
-theorem coeIdeal_span_singleton (x : R) :
-    (↑(Ideal.span {x} : Ideal R) : FractionalIdeal S P) = spanSingleton S (algebraMap R P x) := by
-  ext y
-  refine' (mem_coeIdeal S).trans (Iff.trans _ (mem_spanSingleton S).symm)
-  constructor
-  · rintro ⟨y', hy', rfl⟩
-    obtain ⟨x', rfl⟩ := Submodule.mem_span_singleton.mp hy'
-    use x'
-    rw [smul_eq_mul, RingHom.map_mul, Algebra.smul_def]
-  · rintro ⟨y', rfl⟩
-    refine' ⟨y' * x, Submodule.mem_span_singleton.mpr ⟨y', rfl⟩, _⟩
-    rw [RingHom.map_mul, Algebra.smul_def]
-#align fractional_ideal.coe_ideal_span_singleton FractionalIdeal.coeIdeal_span_singleton
-
-@[simp]
-theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocalization S P']
-    (x : P) :
-    canonicalEquiv S P P' (spanSingleton S x) =
-      spanSingleton S
-        (IsLocalization.map P' (RingHom.id R)
-          (fun y (hy : y ∈ S) => show RingHom.id R y ∈ S from hy) x) := by
-  apply SetLike.ext_iff.mpr
-  intro y
-  constructor <;> intro h
-  · rw [mem_spanSingleton]
-    obtain ⟨x', hx', rfl⟩ := (mem_canonicalEquiv_apply _ _ _).mp h
-    obtain ⟨z, rfl⟩ := (mem_spanSingleton _).mp hx'
-    use z
-    rw [IsLocalization.map_smul, RingHom.id_apply]
-  · rw [mem_canonicalEquiv_apply]
-    obtain ⟨z, rfl⟩ := (mem_spanSingleton _).mp h
-    use z • x
-    use (mem_spanSingleton _).mpr ⟨z, rfl⟩
-    simp [IsLocalization.map_smul]
-#align fractional_ideal.canonical_equiv_span_singleton FractionalIdeal.canonicalEquiv_spanSingleton
-
-theorem mem_singleton_mul {x y : P} {I : FractionalIdeal S P} :
-    y ∈ spanSingleton S x * I ↔ ∃ y' ∈ I, y = x * y' := by
-  constructor
-  · intro h
-    refine FractionalIdeal.mul_induction_on h ?_ ?_
-    · intro x' hx' y' hy'
-      obtain ⟨a, ha⟩ := (mem_spanSingleton S).mp hx'
-      use a • y', Submodule.smul_mem (I : Submodule R P) a hy'
-      rw [← ha, Algebra.mul_smul_comm, Algebra.smul_mul_assoc]
-    · rintro _ _ ⟨y, hy, rfl⟩ ⟨y', hy', rfl⟩
-      exact ⟨y + y', Submodule.add_mem (I : Submodule R P) hy hy', (mul_add _ _ _).symm⟩
-  · rintro ⟨y', hy', rfl⟩
-    exact mul_mem_mul ((mem_spanSingleton S).mpr ⟨1, one_smul _ _⟩) hy'
-#align fractional_ideal.mem_singleton_mul FractionalIdeal.mem_singleton_mul
-
-variable (K)
-
-theorem mk'_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {x y : R₁} (hy : y ∈ R₁⁰) :
-    spanSingleton R₁⁰ (IsLocalization.mk' K x ⟨y, hy⟩) * I = (J : FractionalIdeal R₁⁰ K) ↔
-      Ideal.span {x} * I = Ideal.span {y} * J := by
-  have :
-    spanSingleton R₁⁰ (IsLocalization.mk' _ (1 : R₁) ⟨y, hy⟩) *
-        spanSingleton R₁⁰ (algebraMap R₁ K y) =
-      1 := by
-    rw [spanSingleton_mul_spanSingleton, mul_comm, ← IsLocalization.mk'_eq_mul_mk'_one,
-      IsLocalization.mk'_self, spanSingleton_one]
-  let y' : (FractionalIdeal R₁⁰ K)ˣ := Units.mkOfMulEqOne _ _ this
-  have coe_y' : ↑y' = spanSingleton R₁⁰ (IsLocalization.mk' K (1 : R₁) ⟨y, hy⟩) := rfl
-  refine' Iff.trans _ (y'.mul_right_inj.trans coeIdeal_inj)
-  rw [coe_y', coeIdeal_mul, coeIdeal_span_singleton, coeIdeal_mul, coeIdeal_span_singleton, ←
-    mul_assoc, spanSingleton_mul_spanSingleton, ← mul_assoc, spanSingleton_mul_spanSingleton,
-    mul_comm (mk' _ _ _), ← IsLocalization.mk'_eq_mul_mk'_one, mul_comm (mk' _ _ _), ←
-    IsLocalization.mk'_eq_mul_mk'_one, IsLocalization.mk'_self, spanSingleton_one, one_mul]
-#align fractional_ideal.mk'_mul_coe_ideal_eq_coe_ideal FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal
-
-variable {K}
-
-theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
-    spanSingleton R₁⁰ z * (I : FractionalIdeal R₁⁰ K) = J ↔
-      Ideal.span {((IsLocalization.sec R₁⁰ z).1 : R₁)} * I =
-        Ideal.span {((IsLocalization.sec R₁⁰ z).2 : R₁)} * J := by
-  rw [← mk'_mul_coeIdeal_eq_coeIdeal K (IsLocalization.sec R₁⁰ z).2.prop,
-    IsLocalization.mk'_sec K z]
-#align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal
-
-variable [IsDomain R₁]
-
-theorem one_div_spanSingleton (x : K) : 1 / spanSingleton R₁⁰ x = spanSingleton R₁⁰ x⁻¹ :=
-  if h : x = 0 then by simp [h] else (eq_one_div_of_mul_eq_one_right _ _ (by simp [h])).symm
-#align fractional_ideal.one_div_span_singleton FractionalIdeal.one_div_spanSingleton
-
-@[simp]
-theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
-    J / spanSingleton R₁⁰ d = spanSingleton R₁⁰ d⁻¹ * J := by
-  rw [← one_div_spanSingleton]
-  by_cases hd : d = 0
-  · simp only [hd, spanSingleton_zero, div_zero, zero_mul]
-  have h_spand : spanSingleton R₁⁰ d ≠ 0 := mt spanSingleton_eq_zero_iff.mp hd
-  apply le_antisymm
-  · intro x hx
-    dsimp only [val_eq_coe] at hx ⊢ -- Porting note: get rid of the partially applied `coe`s
-    rw [coe_div h_spand, Submodule.mem_div_iff_forall_mul_mem] at hx
-    specialize hx d (mem_spanSingleton_self R₁⁰ d)
-    have h_xd : x = d⁻¹ * (x * d) := by field_simp
-    rw [coe_mul, one_div_spanSingleton, h_xd]
-    exact Submodule.mul_mem_mul (mem_spanSingleton_self R₁⁰ _) hx
-  · rw [le_div_iff_mul_le h_spand, mul_assoc, mul_left_comm, one_div_spanSingleton,
-      spanSingleton_mul_spanSingleton, inv_mul_cancel hd, spanSingleton_one, mul_one]
-#align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingleton
-
-theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
-    ∃ (a : R₁) (aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI := by
-  obtain ⟨a_inv, nonzero, ha⟩ := I.isFractional
-  have nonzero := mem_nonZeroDivisors_iff_ne_zero.mp nonzero
-  have map_a_nonzero : algebraMap R₁ K a_inv ≠ 0 :=
-    mt IsFractionRing.to_map_eq_zero_iff.mp nonzero
-  refine'
-    ⟨a_inv,
-      Submodule.comap (Algebra.linearMap R₁ K) ↑(spanSingleton R₁⁰ (algebraMap R₁ K a_inv) * I),
-      nonzero, ext fun x => Iff.trans ⟨_, _⟩ mem_singleton_mul.symm⟩
-  · intro hx
-    obtain ⟨x', hx'⟩ := ha x hx
-    rw [Algebra.smul_def] at hx'
-    refine' ⟨algebraMap R₁ K x', (mem_coeIdeal _).mpr ⟨x', mem_singleton_mul.mpr _, rfl⟩, _⟩
-    · exact ⟨x, hx, hx'⟩
-    · rw [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
-  · rintro ⟨y, hy, rfl⟩
-    obtain ⟨x', hx', rfl⟩ := (mem_coeIdeal _).mp hy
-    obtain ⟨y', hy', hx'⟩ := mem_singleton_mul.mp hx'
-    rw [Algebra.linearMap_apply] at hx'
-    rwa [hx', ← mul_assoc, inv_mul_cancel map_a_nonzero, one_mul]
-#align fractional_ideal.exists_eq_span_singleton_mul FractionalIdeal.exists_eq_spanSingleton_mul
-
-instance isPrincipal {R} [CommRing R] [IsDomain R] [IsPrincipalIdealRing R] [Algebra R K]
-    [IsFractionRing R K] (I : FractionalIdeal R⁰ K) : (I : Submodule R K).IsPrincipal := by
-  obtain ⟨a, aI, -, ha⟩ := exists_eq_spanSingleton_mul I
-  use (algebraMap R K a)⁻¹ * algebraMap R K (generator aI)
-  suffices I = spanSingleton R⁰ ((algebraMap R K a)⁻¹ * algebraMap R K (generator aI)) by
-    rw [spanSingleton] at this
-    exact congr_arg Subtype.val this
-  conv_lhs => rw [ha, ← span_singleton_generator aI]
-  rw [Ideal.submodule_span_eq, coeIdeal_span_singleton (generator aI),
-    spanSingleton_mul_spanSingleton]
-#align fractional_ideal.is_principal FractionalIdeal.isPrincipal
-
-theorem le_spanSingleton_mul_iff {x : P} {I J : FractionalIdeal S P} :
-    I ≤ spanSingleton S x * J ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI :=
-  show (∀ {zI} (hzI : zI ∈ I), zI ∈ spanSingleton _ x * J) ↔ ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI by
-    simp only [mem_singleton_mul, eq_comm]
-#align fractional_ideal.le_span_singleton_mul_iff FractionalIdeal.le_spanSingleton_mul_iff
-
-theorem spanSingleton_mul_le_iff {x : P} {I J : FractionalIdeal S P} :
-    spanSingleton _ x * I ≤ J ↔ ∀ z ∈ I, x * z ∈ J := by
-  simp only [mul_le, mem_singleton_mul, mem_spanSingleton]
-  constructor
-  · intro h zI hzI
-    exact h x ⟨1, one_smul _ _⟩ zI hzI
-  · rintro h _ ⟨z, rfl⟩ zI hzI
-    rw [Algebra.smul_mul_assoc]
-    exact Submodule.smul_mem J.1 _ (h zI hzI)
-#align fractional_ideal.span_singleton_mul_le_iff FractionalIdeal.spanSingleton_mul_le_iff
-
-theorem eq_spanSingleton_mul {x : P} {I J : FractionalIdeal S P} :
-    I = spanSingleton _ x * J ↔ (∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI) ∧ ∀ z ∈ J, x * z ∈ I := by
-  simp only [le_antisymm_iff, le_spanSingleton_mul_iff, spanSingleton_mul_le_iff]
-#align fractional_ideal.eq_span_singleton_mul FractionalIdeal.eq_spanSingleton_mul
-
-end PrincipalIdealRing
-
-variable {R₁ : Type*} [CommRing R₁]
-
-variable {K : Type*} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
-
-attribute [local instance] Classical.propDecidable
-
-theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
-  isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by
-    rw [coe_zero, le_bot_iff] at hI
-    rw [hI]
-    exact fg_bot
-#align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
-
-theorem isNoetherian_iff {I : FractionalIdeal R₁⁰ K} :
-    IsNoetherian R₁ I ↔ ∀ J ≤ I, (J : Submodule R₁ K).FG :=
-  isNoetherian_submodule.trans ⟨fun h _ hJ => h _ hJ, fun h J hJ => h ⟨J, isFractional_of_le hJ⟩ hJ⟩
-#align fractional_ideal.is_noetherian_iff FractionalIdeal.isNoetherian_iff
-
-theorem isNoetherian_coeIdeal [IsNoetherianRing R₁] (I : Ideal R₁) :
-    IsNoetherian R₁ (I : FractionalIdeal R₁⁰ K) := by
-  rw [isNoetherian_iff]
-  intro J hJ
-  obtain ⟨J, rfl⟩ := le_one_iff_exists_coeIdeal.mp (le_trans hJ coeIdeal_le_one)
-  exact (IsNoetherian.noetherian J).map _
-#align fractional_ideal.is_noetherian_coe_ideal FractionalIdeal.isNoetherian_coeIdeal
-
-variable [IsDomain R₁]
-
-theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdeal R₁⁰ K}
-    (hI : IsNoetherian R₁ I) :
-    IsNoetherian R₁ (spanSingleton R₁⁰ (algebraMap R₁ K x)⁻¹ * I : FractionalIdeal R₁⁰ K) := by
-  by_cases hx : x = 0
-  · rw [hx, RingHom.map_zero, inv_zero, spanSingleton_zero, zero_mul]
-    exact isNoetherian_zero
-  have h_gx : algebraMap R₁ K x ≠ 0 :=
-    mt ((injective_iff_map_eq_zero (algebraMap R₁ K)).mp (IsFractionRing.injective _ _) x) hx
-  have h_spanx : spanSingleton R₁⁰ (algebraMap R₁ K x) ≠ 0 := spanSingleton_ne_zero_iff.mpr h_gx
-  rw [isNoetherian_iff] at hI ⊢
-  intro J hJ
-  rw [← div_spanSingleton, le_div_iff_mul_le h_spanx] at hJ
-  obtain ⟨s, hs⟩ := hI _ hJ
-  use s * {(algebraMap R₁ K x)⁻¹}
-  rw [Finset.coe_mul, Finset.coe_singleton, ← span_mul_span, hs, ← coe_spanSingleton R₁⁰, ←
-    coe_mul, mul_assoc, spanSingleton_mul_spanSingleton, mul_inv_cancel h_gx, spanSingleton_one,
-    mul_one]
-#align fractional_ideal.is_noetherian_span_singleton_inv_to_map_mul FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul
-
-/-- Every fractional ideal of a noetherian integral domain is noetherian. -/
-theorem isNoetherian [IsNoetherianRing R₁] (I : FractionalIdeal R₁⁰ K) : IsNoetherian R₁ I := by
-  obtain ⟨d, J, _, rfl⟩ := exists_eq_spanSingleton_mul I
-  apply isNoetherian_spanSingleton_inv_to_map_mul
-  apply isNoetherian_coeIdeal
-#align fractional_ideal.is_noetherian FractionalIdeal.isNoetherian
-
-section Adjoin
-
-variable (S)
-variable (x : P) (hx : IsIntegral R x)
-
-/-- `A[x]` is a fractional ideal for every integral `x`. -/
-theorem isFractional_adjoin_integral :
-    IsFractional S (Subalgebra.toSubmodule (Algebra.adjoin R ({x} : Set P))) :=
-  isFractional_of_fg hx.fg_adjoin_singleton
-#align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
-
-/-- `FractionalIdeal.adjoinIntegral (S : Submonoid R) x hx` is `R[x]` as a fractional ideal,
-where `hx` is a proof that `x : P` is integral over `R`. -/
--- Porting note: `@[simps]` generated a `Subtype.val` coercion instead of a
--- `FractionalIdeal.coeToSubmodule` coercion
-def adjoinIntegral : FractionalIdeal S P :=
-  ⟨_, isFractional_adjoin_integral S x hx⟩
-#align fractional_ideal.adjoin_integral FractionalIdeal.adjoinIntegral
-
-@[simp]
-theorem adjoinIntegral_coe :
-    (adjoinIntegral S x hx : Submodule R P) =
-      (Subalgebra.toSubmodule (Algebra.adjoin R ({x} : Set P))) :=
-  rfl
-
-theorem mem_adjoinIntegral_self : x ∈ adjoinIntegral S x hx :=
-  Algebra.subset_adjoin (Set.mem_singleton x)
-#align fractional_ideal.mem_adjoin_integral_self FractionalIdeal.mem_adjoinIntegral_self
-
-end Adjoin
-
 end FractionalIdeal

This PR defines the absolute ideal norm of a fractional ideal I : FractionalIdeal R⁰ K where K is a fraction field of R as a zero-preserving group homomorphism with values in ℚ and proves that it generalises the norm on (integral) ideals (and some other classical result).

Also in this PR:

• Add the directory Mathlib/RingTheory/FractionalIdeal and move the file Mathlib/RingTheory/FractionalIdeal.lean to Mathlib/RingTheory/FractionalIdeal/Basic.lean. The new results are in Mathlib/RingTheory/FractionalIdeal/Norm.lean
• Define the numerator and denominator of a fractional ideal. These are used to define the norm. Also define a linear equiv between a fractional ideal and its numerator.
• Several technical lemmas.

@@ -134,6 +134,40 @@ protected theorem isFractional (I : FractionalIdeal S P) : IsFractional S (I : S
   I.prop
 #align fractional_ideal.is_fractional FractionalIdeal.isFractional
 
+/-- An element of `S` such that `I.den • I = I.num`, see `FractionalIdeal.num` and
+`FractionalIdeal.den_mul_eq_num`. -/
+noncomputable def den (I : FractionalIdeal S P) : S :=
+  ⟨I.2.choose, I.2.choose_spec.1⟩
+
+/-- An ideal of `R` such that `I.den • I = I.num`, see `FractionalIdeal.den` and
+`FractionalIdeal.den_mul_eq_num`. -/
+noncomputable def num (I : FractionalIdeal S P) : Ideal R :=
+  (I.den • (I : Submodule R P)).comap (Algebra.linearMap R P)
+
+theorem den_mul_self_eq_num (I : FractionalIdeal S P) :
+    I.den • (I : Submodule R P) = Submodule.map (Algebra.linearMap R P) I.num := by
+  rw [den, num, Submodule.map_comap_eq]
+  refine (inf_of_le_right ?_).symm
+  rintro _ ⟨a, ha, rfl⟩
+  exact I.2.choose_spec.2 a ha
+
+/-- The linear equivalence between the fractional ideal `I` and the integral ideal `I.num`
+defined by mapping `x` to `den I • x`. -/
+noncomputable def equivNum [Nontrivial P] [NoZeroSMulDivisors R P]
+    {I : FractionalIdeal S P} (h_nz : (I.den : R) ≠ 0) : I ≃ₗ[R] I.num := by
+  refine LinearEquiv.trans
+    (LinearEquiv.ofBijective ((DistribMulAction.toLinearMap R P I.den).restrict fun _ hx ↦ ?_)
+      ⟨fun _ _ hxy ↦ ?_, fun ⟨y, hy⟩ ↦ ?_⟩)
+    (Submodule.equivMapOfInjective (Algebra.linearMap R P)
+      (NoZeroSMulDivisors.algebraMap_injective R P) (num I)).symm
+  · rw [← den_mul_self_eq_num]
+    exact Submodule.smul_mem_pointwise_smul _ _ _ hx
+  · simp_rw [LinearMap.restrict_apply, DistribMulAction.toLinearMap_apply, Subtype.mk.injEq] at hxy
+    rwa [Submonoid.smul_def, Submonoid.smul_def, smul_right_inj h_nz, SetCoe.ext_iff] at hxy
+  · rw [← den_mul_self_eq_num] at hy
+    obtain ⟨x, hx, hxy⟩ := hy
+    exact ⟨⟨x, hx⟩, by simp_rw [LinearMap.restrict_apply, Subtype.ext_iff, ← hxy]; rfl⟩
+
 section SetLike
 
 instance : SetLike (FractionalIdeal S P) P where
@@ -150,6 +184,15 @@ theorem ext {I J : FractionalIdeal S P} : (∀ x, x ∈ I ↔ x ∈ J) → I = J
   SetLike.ext
 #align fractional_ideal.ext FractionalIdeal.ext
 
+@[simp]
+ theorem equivNum_apply [Nontrivial P] [NoZeroSMulDivisors R P] {I : FractionalIdeal S P}
+    (h_nz : (I.den : R) ≠ 0) (x : I) :
+    algebraMap R P (equivNum h_nz x) = I.den • x := by
+  change Algebra.linearMap R P _ = _
+  rw [equivNum, LinearEquiv.trans_apply, LinearEquiv.ofBijective_apply, LinearMap.restrict_apply,
+    Submodule.map_equivMapOfInjective_symm_apply, Subtype.coe_mk,
+    DistribMulAction.toLinearMap_apply]
+
 /-- Copy of a `FractionalIdeal` with a new underlying set equal to the old one.
 Useful to fix definitional equalities. -/
 protected def copy (p : FractionalIdeal S P) (s : Set P) (hs : s = ↑p) : FractionalIdeal S P :=
@@ -337,6 +380,19 @@ instance : Inhabited (FractionalIdeal S P) :=
 instance : One (FractionalIdeal S P) :=
   ⟨(⊤ : Ideal R)⟩
 
+theorem zero_of_num_eq_bot [NoZeroSMulDivisors R P] (hS : 0 ∉ S) {I : FractionalIdeal S P}
+    (hI : I.num = ⊥) : I = 0 := by
+  rw [← coeToSubmodule_eq_bot, eq_bot_iff]
+  intro x hx
+  suffices (den I : R) • x = 0 from
+    (smul_eq_zero.mp this).resolve_left (ne_of_mem_of_not_mem (SetLike.coe_mem _) hS)
+  have h_eq : I.den • (I : Submodule R P) = ⊥ := by rw [den_mul_self_eq_num, hI, Submodule.map_bot]
+  exact (Submodule.eq_bot_iff _).mp h_eq (den I • x) ⟨x, hx, rfl⟩
+
+theorem num_zero_eq (h_inj : Function.Injective (algebraMap R P)) :
+    num (0 : FractionalIdeal S P) = 0 := by
+  simpa [num, LinearMap.ker_eq_bot] using h_inj
+
 variable (S)
 
 @[simp, norm_cast]
@@ -1305,6 +1361,17 @@ theorem mem_spanSingleton_self (x : P) : x ∈ spanSingleton S x :=
   (mem_spanSingleton S).mpr ⟨1, one_smul _ _⟩
 #align fractional_ideal.mem_span_singleton_self FractionalIdeal.mem_spanSingleton_self
 
+/-- A version of `FractionalIdeal.den_mul_self_eq_num` in terms of fractional ideals. -/
+theorem den_mul_self_eq_num' (I : FractionalIdeal S P) :
+    spanSingleton S (algebraMap R P I.den) * I = I.num := by
+  apply coeToSubmodule_injective
+  dsimp only
+  rw [coe_mul, ← smul_eq_mul, coe_spanSingleton, smul_eq_mul, Submodule.span_singleton_mul]
+  convert I.den_mul_self_eq_num using 1
+  ext
+  erw [Set.mem_smul_set, Set.mem_smul_set]
+  simp [Algebra.smul_def]
+
 variable {S}
 
 @[simp]

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -556,7 +556,7 @@ theorem coeIdeal_mul (I J : Ideal R) : (↑(I * J) : FractionalIdeal S P) = I *
   exact coeToSubmodule_injective (coeSubmodule_mul _ _ _)
 #align fractional_ideal.coe_ideal_mul FractionalIdeal.coeIdeal_mul
 
-theorem mul_left_mono (I : FractionalIdeal S P) : Monotone ((· * ·) I) := by
+theorem mul_left_mono (I : FractionalIdeal S P) : Monotone (I * ·) := by
   intro J J' h
   simp only [mul_def]
   exact mul_le.mpr fun x hx y hy => mul_mem_mul hx (h hy)

Zulip

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

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

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

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

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

• Add a lemma Algebra.IsIntegral.of_injective.

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

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

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

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

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

• Golf IsIntegral.tmul and isField_of_isIntegral_of_isField(').

• Combine isIntegral_trans_aux into isIntegral_trans and golf.

• Add Algebra namespace to isIntegral_sup.

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

The next changed file is RingTheory/Algebraic:

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

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

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

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

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

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

@@ -1598,7 +1598,7 @@ variable (x : P) (hx : IsIntegral R x)
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Subalgebra.toSubmodule (Algebra.adjoin R ({x} : Set P))) :=
-  isFractional_of_fg (IsIntegral.fg_adjoin_singleton x hx)
+  isFractional_of_fg hx.fg_adjoin_singleton
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 
 /-- `FractionalIdeal.adjoinIntegral (S : Submonoid R) x hx` is `R[x]` as a fractional ideal,

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

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

This PR makes the following renames:

| From | To |

@@ -1598,7 +1598,7 @@ variable (x : P) (hx : IsIntegral R x)
 /-- `A[x]` is a fractional ideal for every integral `x`. -/
 theorem isFractional_adjoin_integral :
     IsFractional S (Subalgebra.toSubmodule (Algebra.adjoin R ({x} : Set P))) :=
-  isFractional_of_fg (FG_adjoin_singleton_of_integral x hx)
+  isFractional_of_fg (IsIntegral.fg_adjoin_singleton x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 
 /-- `FractionalIdeal.adjoinIntegral (S : Submonoid R) x hx` is `R[x]` as a fractional ideal,

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -916,7 +916,7 @@ theorem canonicalEquiv_symm : (canonicalEquiv S P P').symm = canonicalEquiv S P'
 #align fractional_ideal.canonical_equiv_symm FractionalIdeal.canonicalEquiv_symm
 
 theorem canonicalEquiv_flip (I) : canonicalEquiv S P P' (canonicalEquiv S P' P I) = I := by
-  rw [← canonicalEquiv_symm, RingEquiv.apply_symm_apply]
+  rw [← canonicalEquiv_symm]; erw [RingEquiv.apply_symm_apply]
 #align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flip
 
 @[simp]

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -484,7 +484,7 @@ theorem _root_.IsFractional.nsmul {I : Submodule R P} :
     ∀ n : ℕ, IsFractional S I → IsFractional S (n • I : Submodule R P)
   | 0, _ => by
     rw [zero_smul]
-    convert((0 : Ideal R) : FractionalIdeal S P).isFractional
+    convert ((0 : Ideal R) : FractionalIdeal S P).isFractional
     simp
   | n + 1, h => by
     rw [succ_nsmul]
@@ -943,7 +943,7 @@ theorem canonicalEquiv_coeIdeal (I : Ideal R) : canonicalEquiv S P P' I = I := b
 @[simp]
 theorem canonicalEquiv_self : canonicalEquiv S P P = RingEquiv.refl _ := by
   rw [← canonicalEquiv_trans_canonicalEquiv S P P]
-  convert(canonicalEquiv S P P).symm_trans_self
+  convert (canonicalEquiv S P P).symm_trans_self
   exact (canonicalEquiv_symm S P P).symm
 #align fractional_ideal.canonical_equiv_self FractionalIdeal.canonicalEquiv_self
 

This removes redundant field values of the form add := add for smaller terms and less unfolding during unification.

A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... } where some xi is a field of some aj was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.

Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add and not toFun (though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.

It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.

@@ -191,9 +191,6 @@ theorem coeToSet_coeToSubmodule (I : FractionalIdeal S P) :
 
 /-! Transfer instances from `Submodule R P` to `FractionalIdeal S P`. -/
 
-instance (I : FractionalIdeal S P) : AddCommGroup I :=
-  Submodule.addCommGroup (I : Submodule R P)
-
 instance (I : FractionalIdeal S P) : Module R I :=
   Submodule.module (I : Submodule R P)
 

@@ -550,8 +550,7 @@ theorem mul_def (I J : FractionalIdeal S P) : I * J = ⟨I * J, I.isFractional.m
 
 @[simp, norm_cast]
 theorem coe_mul (I J : FractionalIdeal S P) : (↑(I * J) : Submodule R P) = I * J := by
-  simp only [mul_def]
-  rfl
+  simp only [mul_def, coe_mk]
 #align fractional_ideal.coe_mul FractionalIdeal.coe_mul
 
 @[simp, norm_cast]
@@ -613,7 +612,7 @@ instance commSemiring : CommSemiring (FractionalIdeal S P) :=
 
 variable (S P)
 
-/-- `FractionalIdeal.submodule.has_coe` as a bundled `RingHom`. -/
+/-- `FractionalIdeal.coeToSubmodule` as a bundled `RingHom`. -/
 @[simps]
 def coeSubmoduleHom : FractionalIdeal S P →+* Submodule R P where
   toFun := coeToSubmodule
@@ -717,9 +716,10 @@ theorem _root_.IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
   | ⟨a, a_nonzero, hI⟩ =>
     ⟨a, a_nonzero, fun b hb => by
       obtain ⟨b', b'_mem, hb'⟩ := Submodule.mem_map.mp hb
+      rw [AlgHom.toLinearMap_apply] at hb'
       obtain ⟨x, hx⟩ := hI b' b'_mem
       use x
-      erw [← g.commutes, hx, g.map_smul, hb']⟩
+      rw [← g.commutes, hx, g.map_smul, hb']⟩
 #align is_fractional.map IsFractional.map
 
 /-- `I.map g` is the pushforward of the fractional ideal `I` along the algebra morphism `g` -/
@@ -893,8 +893,7 @@ variable (S P P')
 ideals in `P` and in `P'`, which are both localizations of `R` at `S`. -/
 noncomputable irreducible_def canonicalEquiv : FractionalIdeal S P ≃+* FractionalIdeal S P' :=
   mapEquiv
-    {
-      ringEquivOfRingEquiv P P' (RingEquiv.refl R)
+    { ringEquivOfRingEquiv P P' (RingEquiv.refl R)
         (show S.map _ = S by rw [RingEquiv.toMonoidHom_refl, Submonoid.map_id]) with
       commutes' := fun r => ringEquivOfRingEquiv_eq _ _ }
 #align fractional_ideal.canonical_equiv FractionalIdeal.canonicalEquiv
@@ -971,7 +970,7 @@ variable {I J : FractionalIdeal R⁰ K} (h : K →ₐ[R] K')
 
 /-- Nonzero fractional ideals contain a nonzero integer. -/
 theorem exists_ne_zero_mem_isInteger [Nontrivial R] (hI : I ≠ 0) :
-    ∃ (x : R) (_ : x ≠ 0), algebraMap R K x ∈ I := by
+    ∃ x, x ≠ 0 ∧ algebraMap R K x ∈ I := by
   obtain ⟨y : K, y_mem, y_not_mem⟩ :=
     SetLike.exists_of_lt (by simpa only using bot_lt_iff_ne_bot.mpr hI)
   have y_ne_zero : y ≠ 0 := by simpa using y_not_mem
@@ -1403,8 +1402,7 @@ theorem canonicalEquiv_spanSingleton {P'} [CommRing P'] [Algebra R P'] [IsLocali
     obtain ⟨x', hx', rfl⟩ := (mem_canonicalEquiv_apply _ _ _).mp h
     obtain ⟨z, rfl⟩ := (mem_spanSingleton _).mp hx'
     use z
-    rw [IsLocalization.map_smul]
-    rfl
+    rw [IsLocalization.map_smul, RingHom.id_apply]
   · rw [mem_canonicalEquiv_apply]
     obtain ⟨z, rfl⟩ := (mem_spanSingleton _).mp h
     use z • x
@@ -1452,9 +1450,8 @@ variable {K}
 theorem spanSingleton_mul_coeIdeal_eq_coeIdeal {I J : Ideal R₁} {z : K} :
     spanSingleton R₁⁰ z * (I : FractionalIdeal R₁⁰ K) = J ↔
       Ideal.span {((IsLocalization.sec R₁⁰ z).1 : R₁)} * I =
-        Ideal.span {((IsLocalization.sec R₁⁰ z).2 : R₁)} * J :=
-  by-- `erw` to deal with the distinction between `y` and `⟨y.1, y.2⟩`
-  erw [← mk'_mul_coeIdeal_eq_coeIdeal K (IsLocalization.sec R₁⁰ z).2.prop,
+        Ideal.span {((IsLocalization.sec R₁⁰ z).2 : R₁)} * J := by
+  rw [← mk'_mul_coeIdeal_eq_coeIdeal K (IsLocalization.sec R₁⁰ z).2.prop,
     IsLocalization.mk'_sec K z]
 #align fractional_ideal.span_singleton_mul_coe_ideal_eq_coe_ideal FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal
 
@@ -1550,8 +1547,8 @@ attribute [local instance] Classical.propDecidable
 
 theorem isNoetherian_zero : IsNoetherian R₁ (0 : FractionalIdeal R₁⁰ K) :=
   isNoetherian_submodule.mpr fun I (hI : I ≤ (0 : FractionalIdeal R₁⁰ K)) => by
-    rw [coe_zero] at hI
-    rw [le_bot_iff.mp hI]
+    rw [coe_zero, le_bot_iff] at hI
+    rw [hI]
     exact fg_bot
 #align fractional_ideal.is_noetherian_zero FractionalIdeal.isNoetherian_zero
 

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

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

@@ -1118,7 +1118,7 @@ theorem mem_div_iff_of_nonzero {I J : FractionalIdeal R₁⁰ K} (h : J ≠ 0) {
 
 theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 := by
   by_cases hI : I = 0
-  · rw [hI, div_zero, MulZeroClass.mul_zero]
+  · rw [hI, div_zero, mul_zero]
     exact zero_le 1
   · rw [← coe_le_coe, coe_mul, coe_div hI, coe_one]
     apply Submodule.mul_one_div_le_one
@@ -1127,7 +1127,7 @@ theorem mul_one_div_le_one {I : FractionalIdeal R₁⁰ K} : I * (1 / I) ≤ 1 :
 theorem le_self_mul_one_div {I : FractionalIdeal R₁⁰ K} (hI : I ≤ (1 : FractionalIdeal R₁⁰ K)) :
     I ≤ I * (1 / I) := by
   by_cases hI_nz : I = 0
-  · rw [hI_nz, div_zero, MulZeroClass.mul_zero]
+  · rw [hI_nz, div_zero, mul_zero]
   · rw [← coe_le_coe, coe_mul, coe_div hI_nz, coe_one]
     rw [← coe_le_coe, coe_one] at hI
     exact Submodule.le_self_mul_one_div hI
@@ -1469,7 +1469,7 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
     J / spanSingleton R₁⁰ d = spanSingleton R₁⁰ d⁻¹ * J := by
   rw [← one_div_spanSingleton]
   by_cases hd : d = 0
-  · simp only [hd, spanSingleton_zero, div_zero, MulZeroClass.zero_mul]
+  · simp only [hd, spanSingleton_zero, div_zero, zero_mul]
   have h_spand : spanSingleton R₁⁰ d ≠ 0 := mt spanSingleton_eq_zero_iff.mp hd
   apply le_antisymm
   · intro x hx
@@ -1574,7 +1574,7 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
     (hI : IsNoetherian R₁ I) :
     IsNoetherian R₁ (spanSingleton R₁⁰ (algebraMap R₁ K x)⁻¹ * I : FractionalIdeal R₁⁰ K) := by
   by_cases hx : x = 0
-  · rw [hx, RingHom.map_zero, inv_zero, spanSingleton_zero, MulZeroClass.zero_mul]
+  · rw [hx, RingHom.map_zero, inv_zero, spanSingleton_zero, zero_mul]
     exact isNoetherian_zero
   have h_gx : algebraMap R₁ K x ≠ 0 :=
     mt ((injective_iff_map_eq_zero (algebraMap R₁ K)).mp (IsFractionRing.injective _ _) x) hx

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

This has nice performance benefits.

@@ -77,7 +77,7 @@ open nonZeroDivisors
 
 section Defs
 
-variable {R : Type _} [CommRing R] {S : Submonoid R} {P : Type _} [CommRing P]
+variable {R : Type*} [CommRing R] {S : Submonoid R} {P : Type*} [CommRing P]
 
 variable [Algebra R P]
 
@@ -108,7 +108,7 @@ open Set
 
 open Submodule
 
-variable {R : Type _} [CommRing R] {S : Submonoid R} {P : Type _} [CommRing P]
+variable {R : Type*} [CommRing R] {S : Submonoid R} {P : Type*} [CommRing P]
 
 variable [Algebra R P] [loc : IsLocalization S P]
 
@@ -267,7 +267,7 @@ theorem coeIdeal_le_coeIdeal' [IsLocalization S P] (h : S ≤ nonZeroDivisors R)
 #align fractional_ideal.coe_ideal_le_coe_ideal' FractionalIdeal.coeIdeal_le_coeIdeal'
 
 @[simp]
-theorem coeIdeal_le_coeIdeal (K : Type _) [CommRing K] [Algebra R K] [IsFractionRing R K]
+theorem coeIdeal_le_coeIdeal (K : Type*) [CommRing K] [Algebra R K] [IsFractionRing R K]
     {I J : Ideal R} : (I : FractionalIdeal R⁰ K) ≤ J ↔ I ≤ J :=
   IsFractionRing.coeSubmodule_le_coeSubmodule
 #align fractional_ideal.coe_ideal_le_coe_ideal FractionalIdeal.coeIdeal_le_coeIdeal
@@ -700,7 +700,7 @@ theorem coeIdeal_pow (I : Ideal R) (n : ℕ) : ↑(I ^ n) = (I : FractionalIdeal
 
 open BigOperators
 
-theorem coeIdeal_finprod [IsLocalization S P] {α : Sort _} {f : α → Ideal R}
+theorem coeIdeal_finprod [IsLocalization S P] {α : Sort*} {f : α → Ideal R}
     (hS : S ≤ nonZeroDivisors R) :
     ((∏ᶠ a : α, f a : Ideal R) : FractionalIdeal S P) = ∏ᶠ a : α, (f a : FractionalIdeal S P) :=
   MonoidHom.map_finprod_of_injective (coeIdealHom S P).toMonoidHom (coeIdeal_injective' hS) f
@@ -708,9 +708,9 @@ theorem coeIdeal_finprod [IsLocalization S P] {α : Sort _} {f : α → Ideal R}
 
 end Order
 
-variable {P' : Type _} [CommRing P'] [Algebra R P'] [loc' : IsLocalization S P']
+variable {P' : Type*} [CommRing P'] [Algebra R P'] [loc' : IsLocalization S P']
 
-variable {P'' : Type _} [CommRing P''] [Algebra R P''] [loc'' : IsLocalization S P'']
+variable {P'' : Type*} [CommRing P''] [Algebra R P''] [loc'' : IsLocalization S P'']
 
 theorem _root_.IsFractional.map (g : P →ₐ[R] P') {I : Submodule R P} :
     IsFractional S I → IsFractional S (Submodule.map g.toLinearMap I)
@@ -924,7 +924,7 @@ theorem canonicalEquiv_flip (I) : canonicalEquiv S P P' (canonicalEquiv S P' P I
 #align fractional_ideal.canonical_equiv_flip FractionalIdeal.canonicalEquiv_flip
 
 @[simp]
-theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
+theorem canonicalEquiv_canonicalEquiv (P'' : Type*) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] (I : FractionalIdeal S P) :
     canonicalEquiv S P' P'' (canonicalEquiv S P P' I) = canonicalEquiv S P P'' I := by
   ext
@@ -932,7 +932,7 @@ theorem canonicalEquiv_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P
     exists_prop, exists_exists_and_eq_and]
 #align fractional_ideal.canonical_equiv_canonical_equiv FractionalIdeal.canonicalEquiv_canonicalEquiv
 
-theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type _) [CommRing P''] [Algebra R P'']
+theorem canonicalEquiv_trans_canonicalEquiv (P'' : Type*) [CommRing P''] [Algebra R P'']
     [IsLocalization S P''] :
     (canonicalEquiv S P P').trans (canonicalEquiv S P' P'') = canonicalEquiv S P P'' :=
   RingEquiv.ext (canonicalEquiv_canonicalEquiv S P P' P'')
@@ -963,7 +963,7 @@ i.e. the type `FractionalIdeal R⁰ K` where `IsFractionRing R K`.
 -/
 
 
-variable {K K' : Type _} [Field K] [Field K']
+variable {K K' : Type*} [Field K] [Field K']
 
 variable [Algebra R K] [IsFractionRing R K] [Algebra R K'] [IsFractionRing R K']
 
@@ -1040,7 +1040,7 @@ is a field because `R` is a domain.
 
 open Classical
 
-variable {R₁ : Type _} [CommRing R₁] {K : Type _} [Field K]
+variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
 
 variable [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
@@ -1184,7 +1184,7 @@ theorem mul_div_self_cancel_iff {I : FractionalIdeal R₁⁰ K} : I * (1 / I) =
   ⟨fun h => ⟨1 / I, h⟩, fun ⟨J, hJ⟩ => by rwa [← eq_one_div_of_mul_eq_one_right I J hJ]⟩
 #align fractional_ideal.mul_div_self_cancel_iff FractionalIdeal.mul_div_self_cancel_iff
 
-variable {K' : Type _} [Field K'] [Algebra R₁ K'] [IsFractionRing R₁ K']
+variable {K' : Type*} [Field K'] [Algebra R₁ K'] [IsFractionRing R₁ K']
 
 @[simp]
 theorem map_div (I J : FractionalIdeal R₁⁰ K) (h : K ≃ₐ[R₁] K') :
@@ -1205,7 +1205,7 @@ end Quotient
 
 section Field
 
-variable {R₁ K L : Type _} [CommRing R₁] [Field K] [Field L]
+variable {R₁ K L : Type*} [CommRing R₁] [Field K] [Field L]
 
 variable [Algebra R₁ K] [IsFractionRing R₁ K] [Algebra K L] [IsFractionRing K L]
 
@@ -1234,7 +1234,7 @@ end Field
 
 section PrincipalIdealRing
 
-variable {R₁ : Type _} [CommRing R₁] {K : Type _} [Field K]
+variable {R₁ : Type*} [CommRing R₁] {K : Type*} [Field K]
 
 variable [Algebra R₁ K] [IsFractionRing R₁ K]
 
@@ -1245,7 +1245,7 @@ variable (R₁)
 /-- `FractionalIdeal.span_finset R₁ s f` is the fractional ideal of `R₁` generated by `f '' s`. -/
 -- Porting note: `@[simps]` generated a `Subtype.val` coercion instead of a
 -- `FractionalIdeal.coeToSubmodule` coercion
-def spanFinset {ι : Type _} (s : Finset ι) (f : ι → K) : FractionalIdeal R₁⁰ K :=
+def spanFinset {ι : Type*} (s : Finset ι) (f : ι → K) : FractionalIdeal R₁⁰ K :=
   ⟨Submodule.span R₁ (f '' s), by
     obtain ⟨a', ha'⟩ := IsLocalization.exist_integer_multiples R₁⁰ s f
     refine' ⟨a', a'.2, fun x hx => Submodule.span_induction hx _ _ _ _⟩
@@ -1261,20 +1261,20 @@ def spanFinset {ι : Type _} (s : Finset ι) (f : ι → K) : FractionalIdeal R
       exact IsLocalization.isInteger_smul hx⟩
 #align fractional_ideal.span_finset FractionalIdeal.spanFinset
 
-@[simp] lemma spanFinset_coe {ι : Type _} (s : Finset ι) (f : ι → K) :
+@[simp] lemma spanFinset_coe {ι : Type*} (s : Finset ι) (f : ι → K) :
     (spanFinset R₁ s f : Submodule R₁ K) = Submodule.span R₁ (f '' s) :=
   rfl
 
 variable {R₁}
 
 @[simp]
-theorem spanFinset_eq_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
+theorem spanFinset_eq_zero {ι : Type*} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f = 0 ↔ ∀ j ∈ s, f j = 0 := by
   simp only [← coeToSubmodule_inj, spanFinset_coe, coe_zero, Submodule.span_eq_bot,
     Set.mem_image, Finset.mem_coe, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
 #align fractional_ideal.span_finset_eq_zero FractionalIdeal.spanFinset_eq_zero
 
-theorem spanFinset_ne_zero {ι : Type _} {s : Finset ι} {f : ι → K} :
+theorem spanFinset_ne_zero {ι : Type*} {s : Finset ι} {f : ι → K} :
     spanFinset R₁ s f ≠ 0 ↔ ∃ j ∈ s, f j ≠ 0 := by simp
 #align fractional_ideal.span_finset_ne_zero FractionalIdeal.spanFinset_ne_zero
 
@@ -1542,9 +1542,9 @@ theorem eq_spanSingleton_mul {x : P} {I J : FractionalIdeal S P} :
 
 end PrincipalIdealRing
 
-variable {R₁ : Type _} [CommRing R₁]
+variable {R₁ : Type*} [CommRing R₁]
 
-variable {K : Type _} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
+variable {K : Type*} [Field K] [Algebra R₁ K] [frac : IsFractionRing R₁ K]
 
 attribute [local instance] Classical.propDecidable
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Filippo A. E. Nuccio
-
-! This file was ported from Lean 3 source module ring_theory.fractional_ideal
-! leanprover-community/mathlib commit ed90a7d327c3a5caf65a6faf7e8a0d63c4605df7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Finprod
 import Mathlib.RingTheory.IntegralClosure
@@ -16,6 +11,8 @@ import Mathlib.RingTheory.Noetherian
 import Mathlib.RingTheory.PrincipalIdealDomain
 import Mathlib.Tactic.FieldSimp
 
+#align_import ring_theory.fractional_ideal from "leanprover-community/mathlib"@"ed90a7d327c3a5caf65a6faf7e8a0d63c4605df7"
+
 /-!
 # Fractional ideals
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -1582,7 +1582,7 @@ theorem isNoetherian_spanSingleton_inv_to_map_mul (x : R₁) {I : FractionalIdea
   have h_gx : algebraMap R₁ K x ≠ 0 :=
     mt ((injective_iff_map_eq_zero (algebraMap R₁ K)).mp (IsFractionRing.injective _ _) x) hx
   have h_spanx : spanSingleton R₁⁰ (algebraMap R₁ K x) ≠ 0 := spanSingleton_ne_zero_iff.mpr h_gx
-  rw [isNoetherian_iff] at hI⊢
+  rw [isNoetherian_iff] at hI ⊢
   intro J hJ
   rw [← div_spanSingleton, le_div_iff_mul_le h_spanx] at hJ
   obtain ⟨s, hs⟩ := hI _ hJ

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -121,7 +121,7 @@ This implements the coercion `FractionalIdeal S P → Submodule R P`.
 -/
 @[coe]
 def coeToSubmodule (I : FractionalIdeal S P) : Submodule R P :=
-I.val
+  I.val
 
 /-- Map a fractional ideal `I` to a submodule by forgetting that `∃ a, a I ⊆ R`.
 
@@ -1487,7 +1487,7 @@ theorem div_spanSingleton (J : FractionalIdeal R₁⁰ K) (d : K) :
 #align fractional_ideal.div_span_singleton FractionalIdeal.div_spanSingleton
 
 theorem exists_eq_spanSingleton_mul (I : FractionalIdeal R₁⁰ K) :
-    ∃ (a : R₁)(aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI := by
+    ∃ (a : R₁) (aI : Ideal R₁), a ≠ 0 ∧ I = spanSingleton R₁⁰ (algebraMap R₁ K a)⁻¹ * aI := by
   obtain ⟨a_inv, nonzero, ha⟩ := I.isFractional
   have nonzero := mem_nonZeroDivisors_iff_ne_zero.mp nonzero
   have map_a_nonzero : algebraMap R₁ K a_inv ≠ 0 :=

• An instance from RingTheory.FractionalIdeal was used explicitly so I had to give it a name
• At three places, an equiv is defined and the lemmas produced by [simps] (or [simps!]) make the simpNF linter very unhappy so I commented out the [simps] and left a porting note

@@ -610,7 +610,7 @@ theorem coe_nat_cast (n : ℕ) : ((n : FractionalIdeal S P) : Submodule R P) = n
   by induction n <;> simp [*, Nat.unaryCast]
 #align fractional_ideal.coe_nat_cast FractionalIdeal.coe_nat_cast
 
-instance : CommSemiring (FractionalIdeal S P) :=
+instance commSemiring : CommSemiring (FractionalIdeal S P) :=
   Function.Injective.commSemiring _ Subtype.coe_injective coe_zero coe_one coe_add coe_mul
     (fun _ _ => coe_nsmul _ _) coe_pow coe_nat_cast
 

• Run a non-interactive version of fix-comments.py on all files.
• Go through the diff and manually add/discard/edit chunks.

@@ -366,7 +366,7 @@ variable {S}
 
 /-- `(1 : FractionalIdeal S P)` is defined as the R-submodule `f(R) ≤ P`.
 
-However, this is not definitionally equal to `1 : submodule R P`,
+However, this is not definitionally equal to `1 : Submodule R P`,
 which is proved in the actual `simp` lemma `coe_one`. -/
 theorem coe_one_eq_coeSubmodule_top : ↑(1 : FractionalIdeal S P) = coeSubmodule P (⊤ : Ideal R) :=
   rfl
@@ -380,7 +380,7 @@ theorem coe_one : (↑(1 : FractionalIdeal S P) : Submodule R P) = 1 := by
 section Lattice
 
 /-!
-### `lattice` section
+### `Lattice` section
 
 Defines the order on fractional ideals as inclusion of their underlying sets,
 and ports the lattice structure on submodules to fractional ideals.
@@ -616,7 +616,7 @@ instance : CommSemiring (FractionalIdeal S P) :=
 
 variable (S P)
 
-/-- `FractionalIdeal.submodule.has_coe` as a bundled `ring_hom`. -/
+/-- `FractionalIdeal.submodule.has_coe` as a bundled `RingHom`. -/
 @[simps]
 def coeSubmoduleHom : FractionalIdeal S P →+* Submodule R P where
   toFun := coeToSubmodule
@@ -687,7 +687,7 @@ theorem one_le {I : FractionalIdeal S P} : 1 ≤ I ↔ (1 : P) ∈ I := by
 
 variable (S P)
 
-/-- `coeIdealHom (S : submonoid R) P` is `coe : ideal R → FractionalIdeal S P` as a ring hom -/
+/-- `coeIdealHom (S : Submonoid R) P` is `(↑) : Ideal R → FractionalIdeal S P` as a ring hom -/
 @[simps]
 def coeIdealHom : Ideal R →+* FractionalIdeal S P where
   toFun := coeIdeal
@@ -1610,7 +1610,7 @@ theorem isFractional_adjoin_integral :
   isFractional_of_fg (FG_adjoin_singleton_of_integral x hx)
 #align fractional_ideal.is_fractional_adjoin_integral FractionalIdeal.isFractional_adjoin_integral
 
-/-- `FractionalIdeal.adjoinIntegral (S : submonoid R) x hx` is `R[x]` as a fractional ideal,
+/-- `FractionalIdeal.adjoinIntegral (S : Submonoid R) x hx` is `R[x]` as a fractional ideal,
 where `hx` is a proof that `x : P` is integral over `R`. -/
 -- Porting note: `@[simps]` generated a `Subtype.val` coercion instead of a
 -- `FractionalIdeal.coeToSubmodule` coercion