ring_theory.localization.num_denom ⟷ Mathlib.RingTheory.Localization.NumDen

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

@@ -3,9 +3,9 @@ Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 -/
-import Mathbin.RingTheory.Localization.FractionRing
-import Mathbin.RingTheory.Localization.Integer
-import Mathbin.RingTheory.UniqueFactorizationDomain
+import RingTheory.Localization.FractionRing
+import RingTheory.Localization.Integer
+import RingTheory.UniqueFactorizationDomain
 
 #align_import ring_theory.localization.num_denom from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
 

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

@@ -119,7 +119,7 @@ theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A
   cases' h with d hd
   have d_ne_zero : algebraMap A K (denom A x) ≠ 0 :=
     IsFractionRing.to_map_ne_zero_of_mem_nonZeroDivisors (denom A x).2
-  use ↑d⁻¹ * Num A x
+  use↑d⁻¹ * Num A x
   refine' trans _ (mk'_num_denom A x)
   rw [map_mul, map_units_inv, hd]
   apply mul_left_cancel₀ d_ne_zero

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

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.num_denom
-! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.Localization.FractionRing
 import Mathbin.RingTheory.Localization.Integer
 import Mathbin.RingTheory.UniqueFactorizationDomain
 
+#align_import ring_theory.localization.num_denom from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
+
 /-!
 # Numerator and denominator in a localization
 

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

@@ -42,6 +42,7 @@ variable (A : Type _) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 
 variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
 
+#print IsFractionRing.exists_reduced_fraction /-
 theorem exists_reduced_fraction (x : K) :
     ∃ (a : A) (b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x :=
   by
@@ -55,6 +56,7 @@ theorem exists_reduced_fraction (x : K) :
   simp only [Subtype.coe_mk, RingHom.map_mul, Algebra.smul_def] at *
   erw [← hab, mul_assoc, mk'_spec' _ a' ⟨b', b'_nonzero⟩]
 #align is_fraction_ring.exists_reduced_fraction IsFractionRing.exists_reduced_fraction
+-/
 
 #print IsFractionRing.num /-
 /-- `f.num x` is the numerator of `x : f.codomain` as a reduced fraction. -/
@@ -63,14 +65,18 @@ noncomputable def num (x : K) : A :=
 #align is_fraction_ring.num IsFractionRing.num
 -/
 
+#print IsFractionRing.den /-
 /-- `f.num x` is the denominator of `x : f.codomain` as a reduced fraction. -/
 noncomputable def den (x : K) : nonZeroDivisors A :=
   Classical.choose (Classical.choose_spec (exists_reduced_fraction A x))
 #align is_fraction_ring.denom IsFractionRing.den
+-/
 
+#print IsFractionRing.num_den_reduced /-
 theorem num_den_reduced (x : K) {d} : d ∣ num A x → d ∣ den A x → IsUnit d :=
   (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).1
 #align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reduced
+-/
 
 #print IsFractionRing.mk'_num_den /-
 @[simp]
@@ -81,27 +87,36 @@ theorem mk'_num_den (x : K) : mk' K (num A x) (den A x) = x :=
 
 variable {A}
 
+#print IsFractionRing.num_mul_den_eq_num_iff_eq /-
 theorem num_mul_den_eq_num_iff_eq {x y : K} :
     x * algebraMap A K (den A y) = algebraMap A K (num A y) ↔ x = y :=
   ⟨fun h => by simpa only [mk'_num_denom] using eq_mk'_iff_mul_eq.mpr h, fun h =>
     eq_mk'_iff_mul_eq.mp (by rw [h, mk'_num_denom])⟩
 #align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eq
+-/
 
+#print IsFractionRing.num_mul_den_eq_num_iff_eq' /-
 theorem num_mul_den_eq_num_iff_eq' {x y : K} :
     y * algebraMap A K (den A x) = algebraMap A K (num A x) ↔ x = y :=
   ⟨fun h => by simpa only [eq_comm, mk'_num_denom] using eq_mk'_iff_mul_eq.mpr h, fun h =>
     eq_mk'_iff_mul_eq.mp (by rw [h, mk'_num_denom])⟩
 #align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'
+-/
 
+#print IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq /-
 theorem num_mul_den_eq_num_mul_den_iff_eq {x y : K} :
     num A y * den A x = num A x * den A y ↔ x = y :=
   ⟨fun h => by simpa only [mk'_num_denom] using mk'_eq_of_eq' h, fun h => by rw [h]⟩
 #align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq
+-/
 
+#print IsFractionRing.eq_zero_of_num_eq_zero /-
 theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
   num_mul_den_eq_num_iff_eq'.mp (by rw [MulZeroClass.zero_mul, h, RingHom.map_zero])
 #align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zero
+-/
 
+#print IsFractionRing.isInteger_of_isUnit_den /-
 theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A x :=
   by
   cases' h with d hd
@@ -113,10 +128,13 @@ theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A
   apply mul_left_cancel₀ d_ne_zero
   rw [← mul_assoc, mul_inv_cancel d_ne_zero, one_mul, mk'_spec']
 #align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_den
+-/
 
+#print IsFractionRing.isUnit_den_of_num_eq_zero /-
 theorem isUnit_den_of_num_eq_zero {x : K} (h : num A x = 0) : IsUnit (den A x : A) :=
   num_den_reduced A x (h.symm ▸ dvd_zero _) dvd_rfl
 #align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_den_of_num_eq_zero
+-/
 
 end NumDenom
 

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

@@ -43,7 +43,7 @@ variable (A : Type _) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
 
 theorem exists_reduced_fraction (x : K) :
-    ∃ (a : A)(b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x :=
+    ∃ (a : A) (b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x :=
   by
   obtain ⟨⟨b, b_nonzero⟩, a, hab⟩ := exists_integer_multiple (nonZeroDivisors A) x
   obtain ⟨a', b', c', no_factor, rfl, rfl⟩ :=

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

@@ -42,9 +42,6 @@ variable (A : Type _) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 
 variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
 
-/- warning: is_fraction_ring.exists_reduced_fraction -> IsFractionRing.exists_reduced_fraction is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.exists_reduced_fraction IsFractionRing.exists_reduced_fractionₓ'. -/
 theorem exists_reduced_fraction (x : K) :
     ∃ (a : A)(b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x :=
   by
@@ -66,20 +63,11 @@ noncomputable def num (x : K) : A :=
 #align is_fraction_ring.num IsFractionRing.num
 -/
 
-/- warning: is_fraction_ring.denom -> IsFractionRing.den is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.denom IsFractionRing.denₓ'. -/
 /-- `f.num x` is the denominator of `x : f.codomain` as a reduced fraction. -/
 noncomputable def den (x : K) : nonZeroDivisors A :=
   Classical.choose (Classical.choose_spec (exists_reduced_fraction A x))
 #align is_fraction_ring.denom IsFractionRing.den
 
-/- warning: is_fraction_ring.num_denom_reduced -> IsFractionRing.num_den_reduced is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reducedₓ'. -/
 theorem num_den_reduced (x : K) {d} : d ∣ num A x → d ∣ den A x → IsUnit d :=
   (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).1
 #align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reduced
@@ -93,45 +81,27 @@ theorem mk'_num_den (x : K) : mk' K (num A x) (den A x) = x :=
 
 variable {A}
 
-/- warning: is_fraction_ring.num_mul_denom_eq_num_iff_eq -> IsFractionRing.num_mul_den_eq_num_iff_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eqₓ'. -/
 theorem num_mul_den_eq_num_iff_eq {x y : K} :
     x * algebraMap A K (den A y) = algebraMap A K (num A y) ↔ x = y :=
   ⟨fun h => by simpa only [mk'_num_denom] using eq_mk'_iff_mul_eq.mpr h, fun h =>
     eq_mk'_iff_mul_eq.mp (by rw [h, mk'_num_denom])⟩
 #align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eq
 
-/- warning: is_fraction_ring.num_mul_denom_eq_num_iff_eq' -> IsFractionRing.num_mul_den_eq_num_iff_eq' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'ₓ'. -/
 theorem num_mul_den_eq_num_iff_eq' {x y : K} :
     y * algebraMap A K (den A x) = algebraMap A K (num A x) ↔ x = y :=
   ⟨fun h => by simpa only [eq_comm, mk'_num_denom] using eq_mk'_iff_mul_eq.mpr h, fun h =>
     eq_mk'_iff_mul_eq.mp (by rw [h, mk'_num_denom])⟩
 #align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'
 
-/- warning: is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq -> IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eqₓ'. -/
 theorem num_mul_den_eq_num_mul_den_iff_eq {x y : K} :
     num A y * den A x = num A x * den A y ↔ x = y :=
   ⟨fun h => by simpa only [mk'_num_denom] using mk'_eq_of_eq' h, fun h => by rw [h]⟩
 #align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq
 
-/- warning: is_fraction_ring.eq_zero_of_num_eq_zero -> IsFractionRing.eq_zero_of_num_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K}, (Eq.{succ u1} A (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u1} A 0 (OfNat.mk.{u1} A 0 (Zero.zero.{u1} A (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_5)))))))))) -> (Eq.{succ u2} K x (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_8)))))))))))
-but is expected to have type
-  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (Eq.{succ u2} A (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)))))) -> (Eq.{succ u1} K x (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_8)))))))
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zeroₓ'. -/
 theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
   num_mul_den_eq_num_iff_eq'.mp (by rw [MulZeroClass.zero_mul, h, RingHom.map_zero])
 #align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zero
 
-/- warning: is_fraction_ring.is_integer_of_is_unit_denom -> IsFractionRing.isInteger_of_isUnit_den is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_denₓ'. -/
 theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A x :=
   by
   cases' h with d hd
@@ -144,9 +114,6 @@ theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A
   rw [← mul_assoc, mul_inv_cancel d_ne_zero, one_mul, mk'_spec']
 #align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_den
 
-/- warning: is_fraction_ring.is_unit_denom_of_num_eq_zero -> IsFractionRing.isUnit_den_of_num_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_den_of_num_eq_zeroₓ'. -/
 theorem isUnit_den_of_num_eq_zero {x : K} (h : num A x = 0) : IsUnit (den A x : A) :=
   num_den_reduced A x (h.symm ▸ dvd_zero _) dvd_rfl
 #align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_den_of_num_eq_zero

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

@@ -43,10 +43,7 @@ variable (A : Type _) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
 
 /- warning: is_fraction_ring.exists_reduced_fraction -> IsFractionRing.exists_reduced_fraction is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.exists_reduced_fraction IsFractionRing.exists_reduced_fractionₓ'. -/
 theorem exists_reduced_fraction (x : K) :
     ∃ (a : A)(b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x :=
@@ -81,10 +78,7 @@ noncomputable def den (x : K) : nonZeroDivisors A :=
 #align is_fraction_ring.denom IsFractionRing.den
 
 /- warning: is_fraction_ring.num_denom_reduced -> IsFractionRing.num_den_reduced is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reducedₓ'. -/
 theorem num_den_reduced (x : K) {d} : d ∣ num A x → d ∣ den A x → IsUnit d :=
   (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).1
@@ -100,10 +94,7 @@ theorem mk'_num_den (x : K) : mk' K (num A x) (den A x) = x :=
 variable {A}
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eqₓ'. -/
 theorem num_mul_den_eq_num_iff_eq {x y : K} :
     x * algebraMap A K (den A y) = algebraMap A K (num A y) ↔ x = y :=
@@ -112,10 +103,7 @@ theorem num_mul_den_eq_num_iff_eq {x y : K} :
 #align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'ₓ'. -/
 theorem num_mul_den_eq_num_iff_eq' {x y : K} :
     y * algebraMap A K (den A x) = algebraMap A K (num A x) ↔ x = y :=
@@ -124,10 +112,7 @@ theorem num_mul_den_eq_num_iff_eq' {x y : K} :
 #align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'
 
 /- warning: is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq -> IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eqₓ'. -/
 theorem num_mul_den_eq_num_mul_den_iff_eq {x y : K} :
     num A y * den A x = num A x * den A y ↔ x = y :=
@@ -145,10 +130,7 @@ theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
 #align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zero
 
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 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_denₓ'. -/
 theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A x :=
   by
@@ -163,10 +145,7 @@ theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A
 #align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_den
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_den_of_num_eq_zeroₓ'. -/
 theorem isUnit_den_of_num_eq_zero {x : K} (h : num A x = 0) : IsUnit (den A x : A) :=
   num_den_reduced A x (h.symm ▸ dvd_zero _) dvd_rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -103,7 +103,7 @@ variable {A}
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (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_8))))) x (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) 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_inst_8))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) (Eq.{succ u2} K x y)
 but is expected to have type
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(Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) (Eq.{succ u2} K x y)
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) K (instHMul.{u2} K (NonUnitalNonAssocRing.toMul.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))))) x (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) (Eq.{succ u2} K x y)
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eqₓ'. -/
 theorem num_mul_den_eq_num_iff_eq {x y : K} :
     x * algebraMap A K (den A y) = algebraMap A K (num A y) ↔ x = y :=
@@ -115,7 +115,7 @@ theorem num_mul_den_eq_num_iff_eq {x y : K} :
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (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_8))))) y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))) _inst_9) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A 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Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A 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(CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (Eq.{succ u2} K x y)
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A 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(RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (Eq.{succ u2} K x y)
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) K (instHMul.{u2} K (NonUnitalNonAssocRing.toMul.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))))) y (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (Eq.{succ u2} K x y)
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'ₓ'. -/
 theorem num_mul_den_eq_num_iff_eq' {x y : K} :
     y * algebraMap A K (den A x) = algebraMap A K (num A x) ↔ x = y :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -46,7 +46,7 @@ variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
 lean 3 declaration is
   forall (A : Type.{u1}) [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] (x : K), Exists.{succ u1} A (fun (a : A) => Exists.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) (fun (b : coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) => And (forall {d : A}, (Dvd.Dvd.{u1} A (semigroupDvd.{u1} A (SemigroupWithZero.toSemigroup.{u1} A (NonUnitalSemiring.toSemigroupWithZero.{u1} A (NonUnitalRing.toNonUnitalSemiring.{u1} A (NonUnitalCommRing.toNonUnitalRing.{u1} A (CommRing.toNonUnitalCommRing.{u1} A _inst_5)))))) d a) -> (Dvd.Dvd.{u1} A (semigroupDvd.{u1} A (SemigroupWithZero.toSemigroup.{u1} A (NonUnitalSemiring.toSemigroupWithZero.{u1} A (NonUnitalRing.toNonUnitalSemiring.{u1} A (NonUnitalCommRing.toNonUnitalRing.{u1} A (CommRing.toNonUnitalCommRing.{u1} A _inst_5)))))) d ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A 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(Ring.toMonoid.{u1} A (CommRing.toRing.{u1} A _inst_5)) d)) (Eq.{succ u2} K (IsLocalization.mk'.{u1, u2} A (CommRing.toCommSemiring.{u1} A _inst_5) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)) _inst_9 _inst_10 a b) x)))
 but is expected to have type
-  forall (A : Type.{u2}) [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] (x : K), Exists.{succ u2} A (fun (a : A) => Exists.{succ u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))))))) x (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (fun (b : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))))))) x (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) => And (forall {d : A}, (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalRing.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d a) -> (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalRing.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) b)) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) d)) (Eq.{succ u1} K (IsLocalization.mk'.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_5) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)) _inst_9 _inst_10 a b) x)))
+  forall (A : Type.{u2}) [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] (x : K), Exists.{succ u2} A (fun (a : A) => Exists.{succ u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))))))) x (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (fun (b : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))))))) x (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) => And (forall {d : A}, (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d a) -> (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) b)) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))) d)) (Eq.{succ u1} K (IsLocalization.mk'.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_5) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)) _inst_9 _inst_10 a b) x)))
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.exists_reduced_fraction IsFractionRing.exists_reduced_fractionₓ'. -/
 theorem exists_reduced_fraction (x : K) :
     ∃ (a : A)(b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x :=
@@ -73,7 +73,7 @@ noncomputable def num (x : K) : A :=
 lean 3 declaration is
   forall (A : Type.{u1}) [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9], K -> (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))
 but is expected to have type
-  forall (A : Type.{u1}) [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9], K -> (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))
+  forall (A : Type.{u1}) [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9], K -> (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))))
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.denom IsFractionRing.denₓ'. -/
 /-- `f.num x` is the denominator of `x : f.codomain` as a reduced fraction. -/
 noncomputable def den (x : K) : nonZeroDivisors A :=
@@ -84,7 +84,7 @@ noncomputable def den (x : K) : nonZeroDivisors A :=
 lean 3 declaration is
   forall (A : Type.{u1}) [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] (x : K) {d : A}, (Dvd.Dvd.{u1} A (semigroupDvd.{u1} A (SemigroupWithZero.toSemigroup.{u1} A (NonUnitalSemiring.toSemigroupWithZero.{u1} A (NonUnitalRing.toNonUnitalSemiring.{u1} A (NonUnitalCommRing.toNonUnitalRing.{u1} A (CommRing.toNonUnitalCommRing.{u1} A _inst_5)))))) d (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)) -> (Dvd.Dvd.{u1} A (semigroupDvd.{u1} A (SemigroupWithZero.toSemigroup.{u1} A (NonUnitalSemiring.toSemigroupWithZero.{u1} A (NonUnitalRing.toNonUnitalSemiring.{u1} A (NonUnitalCommRing.toNonUnitalRing.{u1} A (CommRing.toNonUnitalCommRing.{u1} A _inst_5)))))) d ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeSubtype.{succ u1} A (fun (x : A) => Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsUnit.{u1} A (Ring.toMonoid.{u1} A (CommRing.toRing.{u1} A _inst_5)) d)
 but is expected to have type
-  forall (A : Type.{u2}) [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] (x : K) {d : A}, (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalRing.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)) -> (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalRing.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) d)
+  forall (A : Type.{u2}) [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] (x : K) {d : A}, (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)) -> (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))) d)
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reducedₓ'. -/
 theorem num_den_reduced (x : K) {d} : d ∣ num A x → d ∣ den A x → IsUnit d :=
   (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).1
@@ -103,7 +103,7 @@ variable {A}
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (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_8))))) x (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))) _inst_9) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeSubtype.{succ u1} A (fun (x : A) => Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) (Eq.{succ u2} K x y)
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) K (instHMul.{u2} K (NonUnitalNonAssocRing.toMul.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))))) x (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) (Eq.{succ u2} K x y)
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) K (instHMul.{u2} K (NonUnitalNonAssocRing.toMul.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))))) x (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y))) (Eq.{succ u2} K x y)
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eqₓ'. -/
 theorem num_mul_den_eq_num_iff_eq {x y : K} :
     x * algebraMap A K (den A y) = algebraMap A K (num A y) ↔ x = y :=
@@ -115,7 +115,7 @@ theorem num_mul_den_eq_num_iff_eq {x y : K} :
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (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_8))))) y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))) _inst_9) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeSubtype.{succ u1} A (fun (x : A) => Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (Eq.{succ u2} K x y)
 but is expected to have type
-  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) K (instHMul.{u2} K (NonUnitalNonAssocRing.toMul.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))))) y (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (Eq.{succ u2} K x y)
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) K (instHMul.{u2} K (NonUnitalNonAssocRing.toMul.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))))) y (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))))) A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))) (RingHom.instRingHomClassRingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8))) _inst_9) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (Eq.{succ u2} K x y)
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'ₓ'. -/
 theorem num_mul_den_eq_num_iff_eq' {x y : K} :
     y * algebraMap A K (den A x) = algebraMap A K (num A x) ↔ x = y :=
@@ -127,7 +127,7 @@ theorem num_mul_den_eq_num_iff_eq' {x y : K} :
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (Distrib.toHasMul.{u1} A (Ring.toDistrib.{u1} A (CommRing.toRing.{u1} A _inst_5)))) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A 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Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A 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(CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (Distrib.toHasMul.{u1} A (Ring.toDistrib.{u1} A (CommRing.toRing.{u1} A _inst_5)))) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeSubtype.{succ u1} A (fun (x : A) => Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (Eq.{succ u2} K x y)
 but is expected to have type
-  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_5))))) (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_5))))) (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (Eq.{succ u1} K x y)
+  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_5))))) (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_5))))) (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y)))) (Eq.{succ u1} K x y)
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eqₓ'. -/
 theorem num_mul_den_eq_num_mul_den_iff_eq {x y : K} :
     num A y * den A x = num A x * den A y ↔ x = y :=
@@ -138,7 +138,7 @@ theorem num_mul_den_eq_num_mul_den_iff_eq {x y : K} :
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K}, (Eq.{succ u1} A (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u1} A 0 (OfNat.mk.{u1} A 0 (Zero.zero.{u1} A (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_5)))))))))) -> (Eq.{succ u2} K x (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_8)))))))))))
 but is expected to have type
-  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (Eq.{succ u2} A (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)))))) -> (Eq.{succ u1} K x (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_8)))))))
+  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (Eq.{succ u2} A (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)))))) -> (Eq.{succ u1} K x (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_8)))))))
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zeroₓ'. -/
 theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
   num_mul_den_eq_num_iff_eq'.mp (by rw [MulZeroClass.zero_mul, h, RingHom.map_zero])
@@ -148,7 +148,7 @@ theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K}, (IsUnit.{u1} A (Ring.toMonoid.{u1} A (CommRing.toRing.{u1} A _inst_5)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeSubtype.{succ u1} A (fun (x : A) => Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsLocalization.IsInteger.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9 x)
 but is expected to have type
-  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsLocalization.IsInteger.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9 x)
+  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsLocalization.IsInteger.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9 x)
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_denₓ'. -/
 theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A x :=
   by
@@ -166,7 +166,7 @@ theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A
 lean 3 declaration is
   forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K}, (Eq.{succ u1} A (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u1} A 0 (OfNat.mk.{u1} A 0 (Zero.zero.{u1} A (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_5)))))))))) -> (IsUnit.{u1} A (Ring.toMonoid.{u1} A (CommRing.toRing.{u1} A _inst_5)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeSubtype.{succ u1} A (fun (x : A) => Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))
 but is expected to have type
-  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (Eq.{succ u2} A (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)))))) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))
+  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (Eq.{succ u2} A (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)))))) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))
 Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_den_of_num_eq_zeroₓ'. -/
 theorem isUnit_den_of_num_eq_zero {x : K} (h : num A x = 0) : IsUnit (den A x : A) :=
   num_den_reduced A x (h.symm ▸ dvd_zero _) dvd_rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
 
 ! This file was ported from Lean 3 source module ring_theory.localization.num_denom
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
+! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.UniqueFactorizationDomain
 /-!
 # Numerator and denominator in a localization
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Implementation notes
 
 See `src/ring_theory/localization/basic.lean` for a design overview.

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -39,6 +39,12 @@ variable (A : Type _) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 
 variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
 
+/- warning: is_fraction_ring.exists_reduced_fraction -> IsFractionRing.exists_reduced_fraction is a dubious translation:
+lean 3 declaration is
+  forall (A : Type.{u1}) [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] (x : K), Exists.{succ u1} A (fun (a : A) => Exists.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A 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(Ring.toMonoid.{u1} A (CommRing.toRing.{u1} A _inst_5)) d)) (Eq.{succ u2} K (IsLocalization.mk'.{u1, u2} A (CommRing.toCommSemiring.{u1} A _inst_5) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))) K (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)) _inst_9 _inst_10 a b) x)))
+but is expected to have type
+  forall (A : Type.{u2}) [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] (x : K), Exists.{succ u2} A (fun (a : A) => Exists.{succ u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))))))) x (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (fun (b : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))))))) x (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) => And (forall {d : A}, (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalRing.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d a) -> (Dvd.dvd.{u2} A (semigroupDvd.{u2} A (SemigroupWithZero.toSemigroup.{u2} A (NonUnitalSemiring.toSemigroupWithZero.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (NonUnitalCommRing.toNonUnitalRing.{u2} A (CommRing.toNonUnitalCommRing.{u2} A _inst_5)))))) d (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) b)) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) d)) (Eq.{succ u1} K (IsLocalization.mk'.{u2, u1} A (CommRing.toCommSemiring.{u2} A _inst_5) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)) _inst_9 _inst_10 a b) x)))
+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.exists_reduced_fraction IsFractionRing.exists_reduced_fractionₓ'. -/
 theorem exists_reduced_fraction (x : K) :
     ∃ (a : A)(b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x :=
   by
@@ -53,49 +59,95 @@ theorem exists_reduced_fraction (x : K) :
   erw [← hab, mul_assoc, mk'_spec' _ a' ⟨b', b'_nonzero⟩]
 #align is_fraction_ring.exists_reduced_fraction IsFractionRing.exists_reduced_fraction
 
+#print IsFractionRing.num /-
 /-- `f.num x` is the numerator of `x : f.codomain` as a reduced fraction. -/
 noncomputable def num (x : K) : A :=
   Classical.choose (exists_reduced_fraction A x)
 #align is_fraction_ring.num IsFractionRing.num
+-/
 
+/- warning: is_fraction_ring.denom -> IsFractionRing.den is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.denom IsFractionRing.denₓ'. -/
 /-- `f.num x` is the denominator of `x : f.codomain` as a reduced fraction. -/
-noncomputable def denom (x : K) : nonZeroDivisors A :=
+noncomputable def den (x : K) : nonZeroDivisors A :=
   Classical.choose (Classical.choose_spec (exists_reduced_fraction A x))
-#align is_fraction_ring.denom IsFractionRing.denom
-
-theorem num_denom_reduced (x : K) {d} : d ∣ num A x → d ∣ denom A x → IsUnit d :=
+#align is_fraction_ring.denom IsFractionRing.den
+
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+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reducedₓ'. -/
+theorem num_den_reduced (x : K) {d} : d ∣ num A x → d ∣ den A x → IsUnit d :=
   (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).1
-#align is_fraction_ring.num_denom_reduced IsFractionRing.num_denom_reduced
+#align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reduced
 
+#print IsFractionRing.mk'_num_den /-
 @[simp]
-theorem mk'_num_denom (x : K) : mk' K (num A x) (denom A x) = x :=
+theorem mk'_num_den (x : K) : mk' K (num A x) (den A x) = x :=
   (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).2
-#align is_fraction_ring.mk'_num_denom IsFractionRing.mk'_num_denom
+#align is_fraction_ring.mk'_num_denom IsFractionRing.mk'_num_den
+-/
 
 variable {A}
 
-theorem num_mul_denom_eq_num_iff_eq {x y : K} :
-    x * algebraMap A K (denom A y) = algebraMap A K (num A y) ↔ x = y :=
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eqₓ'. -/
+theorem num_mul_den_eq_num_iff_eq {x y : K} :
+    x * algebraMap A K (den A y) = algebraMap A K (num A y) ↔ x = y :=
   ⟨fun h => by simpa only [mk'_num_denom] using eq_mk'_iff_mul_eq.mpr h, fun h =>
     eq_mk'_iff_mul_eq.mp (by rw [h, mk'_num_denom])⟩
-#align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_denom_eq_num_iff_eq
-
-theorem num_mul_denom_eq_num_iff_eq' {x y : K} :
-    y * algebraMap A K (denom A x) = algebraMap A K (num A x) ↔ x = y :=
+#align is_fraction_ring.num_mul_denom_eq_num_iff_eq IsFractionRing.num_mul_den_eq_num_iff_eq
+
+/- warning: is_fraction_ring.num_mul_denom_eq_num_iff_eq' -> IsFractionRing.num_mul_den_eq_num_iff_eq' is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (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_8))))) y (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5))) 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+but is expected to have type
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u2} K (HMul.hMul.{u2, u2, u2} K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A 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+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'ₓ'. -/
+theorem num_mul_den_eq_num_iff_eq' {x y : K} :
+    y * algebraMap A K (den A x) = algebraMap A K (num A x) ↔ x = y :=
   ⟨fun h => by simpa only [eq_comm, mk'_num_denom] using eq_mk'_iff_mul_eq.mpr h, fun h =>
     eq_mk'_iff_mul_eq.mp (by rw [h, mk'_num_denom])⟩
-#align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_denom_eq_num_iff_eq'
-
-theorem num_mul_denom_eq_num_mul_denom_iff_eq {x y : K} :
-    num A y * denom A x = num A x * denom A y ↔ x = y :=
+#align is_fraction_ring.num_mul_denom_eq_num_iff_eq' IsFractionRing.num_mul_den_eq_num_iff_eq'
+
+/- warning: is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq -> IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K} {y : K}, Iff (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (Distrib.toHasMul.{u1} A (Ring.toDistrib.{u1} A (CommRing.toRing.{u1} A _inst_5)))) (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 y) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eqₓ'. -/
+theorem num_mul_den_eq_num_mul_den_iff_eq {x y : K} :
+    num A y * den A x = num A x * den A y ↔ x = y :=
   ⟨fun h => by simpa only [mk'_num_denom] using mk'_eq_of_eq' h, fun h => by rw [h]⟩
-#align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_denom_eq_num_mul_denom_iff_eq
-
+#align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq
+
+/- warning: is_fraction_ring.eq_zero_of_num_eq_zero -> IsFractionRing.eq_zero_of_num_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K}, (Eq.{succ u1} A (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u1} A 0 (OfNat.mk.{u1} A 0 (Zero.zero.{u1} A (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_5)))))))))) -> (Eq.{succ u2} K x (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_8)))))))))))
+but is expected to have type
+  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (Eq.{succ u2} A (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)))))) -> (Eq.{succ u1} K x (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_8)))))))
+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zeroₓ'. -/
 theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
-  num_mul_denom_eq_num_iff_eq'.mp (by rw [MulZeroClass.zero_mul, h, RingHom.map_zero])
+  num_mul_den_eq_num_iff_eq'.mp (by rw [MulZeroClass.zero_mul, h, RingHom.map_zero])
 #align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zero
 
-theorem isInteger_of_isUnit_denom {x : K} (h : IsUnit (denom A x : A)) : IsInteger A x :=
+/- warning: is_fraction_ring.is_integer_of_is_unit_denom -> IsFractionRing.isInteger_of_isUnit_den is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K}, (IsUnit.{u1} A (Ring.toMonoid.{u1} A (CommRing.toRing.{u1} A _inst_5)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))) A (coeSubtype.{succ u1} A (fun (x : A) => Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))) x (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))))))))) (IsFractionRing.den.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsLocalization.IsInteger.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9 x)
+but is expected to have type
+  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x))) -> (IsLocalization.IsInteger.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9 x)
+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_denₓ'. -/
+theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A x :=
   by
   cases' h with d hd
   have d_ne_zero : algebraMap A K (denom A x) ≠ 0 :=
@@ -105,11 +157,17 @@ theorem isInteger_of_isUnit_denom {x : K} (h : IsUnit (denom A x : A)) : IsInteg
   rw [map_mul, map_units_inv, hd]
   apply mul_left_cancel₀ d_ne_zero
   rw [← mul_assoc, mul_inv_cancel d_ne_zero, one_mul, mk'_spec']
-#align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_denom
-
-theorem isUnit_denom_of_num_eq_zero {x : K} (h : num A x = 0) : IsUnit (denom A x : A) :=
-  num_denom_reduced A x (h.symm ▸ dvd_zero _) dvd_rfl
-#align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_denom_of_num_eq_zero
+#align is_fraction_ring.is_integer_of_is_unit_denom IsFractionRing.isInteger_of_isUnit_den
+
+/- warning: is_fraction_ring.is_unit_denom_of_num_eq_zero -> IsFractionRing.isUnit_den_of_num_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_5 : CommRing.{u1} A] [_inst_6 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u1} A (IsDomain.toCancelCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_5) _inst_6)] {K : Type.{u2}} [_inst_8 : Field.{u2} K] [_inst_9 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_5) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_8)))] [_inst_10 : IsFractionRing.{u1, u2} A _inst_5 K (Field.toCommRing.{u2} K _inst_8) _inst_9] {x : K}, (Eq.{succ u1} A (IsFractionRing.num.{u1, u2} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u1} A 0 (OfNat.mk.{u1} A 0 (Zero.zero.{u1} A (MulZeroClass.toHasZero.{u1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_5)))))))))) 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+but is expected to have type
+  forall {A : Type.{u2}} [_inst_5 : CommRing.{u2} A] [_inst_6 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5))] [_inst_7 : UniqueFactorizationMonoid.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)] {K : Type.{u1}} [_inst_8 : Field.{u1} K] [_inst_9 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_5) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_8)))] [_inst_10 : IsFractionRing.{u2, u1} A _inst_5 K (Field.toCommRing.{u1} K _inst_8) _inst_9] {x : K}, (Eq.{succ u2} A (IsFractionRing.num.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x) (OfNat.ofNat.{u2} A 0 (Zero.toOfNat0.{u2} A (CommMonoidWithZero.toZero.{u2} A (CancelCommMonoidWithZero.toCommMonoidWithZero.{u2} A (IsDomain.toCancelCommMonoidWithZero.{u2} A (CommRing.toCommSemiring.{u2} A _inst_5) _inst_6)))))) -> (IsUnit.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_5)))))) (IsFractionRing.den.{u2, u1} A _inst_5 _inst_6 _inst_7 K _inst_8 _inst_9 _inst_10 x)))
+Case conversion may be inaccurate. Consider using '#align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_den_of_num_eq_zeroₓ'. -/
+theorem isUnit_den_of_num_eq_zero {x : K} (h : num A x = 0) : IsUnit (den A x : A) :=
+  num_den_reduced A x (h.symm ▸ dvd_zero _) dvd_rfl
+#align is_fraction_ring.is_unit_denom_of_num_eq_zero IsFractionRing.isUnit_den_of_num_eq_zero
 
 end NumDenom
 

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

@@ -92,7 +92,7 @@ theorem num_mul_denom_eq_num_mul_denom_iff_eq {x y : K} :
 #align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_denom_eq_num_mul_denom_iff_eq
 
 theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
-  num_mul_denom_eq_num_iff_eq'.mp (by rw [zero_mul, h, RingHom.map_zero])
+  num_mul_denom_eq_num_iff_eq'.mp (by rw [MulZeroClass.zero_mul, h, RingHom.map_zero])
 #align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zero
 
 theorem isInteger_of_isUnit_denom {x : K} (h : IsUnit (denom A x : A)) : IsInteger A x :=

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

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)

@@ -23,7 +23,6 @@ commutative ring, field of fractions
 
 
 variable {R : Type*} [CommRing R] (M : Submonoid R) {S : Type*} [CommRing S]
-
 variable [Algebra R S] {P : Type*} [CommRing P]
 
 namespace IsFractionRing
@@ -33,7 +32,6 @@ open IsLocalization
 section NumDen
 
 variable (A : Type*) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
-
 variable {K : Type*} [Field K] [Algebra A K] [IsFractionRing A K]
 
 theorem exists_reduced_fraction (x : K) :

• Introduce typeclass DecompositionMonoid, which says every element in the monoid is primal, i.e., whenever an element divides a product b * c, it can be factored into a product such that the factors divides b and c respectively. A domain is called pre-Schreier if its multiplicative monoid is a decomposition monoid, and these are more general than GCD domains.

• Show that any GCDMonoid is a DecompositionMonoid. In order for lemmas about DecompositionMonoids to automatically apply to UniqueFactorizationMonoids, we add instances from UniqueFactorizationMonoid α to Nonempty (NormalizedGCDMonoid α) to Nonempty (GCDMonoid α) to DecompositionMonoid α. (Zulip) See the bottom of message for an updated diagram of classes and instances.

• Introduce binary predicate IsRelPrime which says that the only common divisors of the two elements are units. Replace previous occurrences in mathlib by this predicate.

• Duplicate all lemmas about IsCoprime in Coprime/Basic (except three lemmas about smul) to IsRelPrime. Due to import constraints, they are spread into three files Algebra/Divisibility/Units (including key lemmas assuming DecompositionMonoid), GroupWithZero/Divisibility, and Coprime/Basic.

• Show IsCoprime always imply IsRelPrime and is equivalent to it in Bezout rings. To reduce duplication, the definition of Bezout rings and the GCDMonoid instance are moved from RingTheory/Bezout to RingTheory/PrincipalIdealDomain, and some results in PrincipalIdealDomain are generalized to Bezout rings.

• Remove the recently added file Squarefree/UniqueFactorizationMonoid and place the results appropriately within Squarefree/Basic. All results are generalized to DecompositionMonoid or weaker except the last one.

Zulip

With this PR, all the following instances (indicated by arrows) now work; this PR fills the central part.

                                                                          EuclideanDomain (bundled)
                                                                              ↙          ↖
                                                                 IsPrincipalIdealRing ← Field (bundled)
                                                                            ↓             ↓
         NormalizationMonoid ←          NormalizedGCDMonoid → GCDMonoid  IsBezout ← ValuationRing ← DiscreteValuationRing
                   ↓                             ↓                 ↘       ↙
Nonempty NormalizationMonoid ← Nonempty NormalizedGCDMonoid →  Nonempty GCDMonoid → IsIntegrallyClosed
                                                 ↑                    ↓
                    WfDvdMonoid ← UniqueFactorizationMonoid → DecompositionMonoid
                                                 ↑
                                       IsPrincipalIdealRing

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -37,7 +37,7 @@ variable (A : Type*) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 variable {K : Type*} [Field K] [Algebra A K] [IsFractionRing A K]
 
 theorem exists_reduced_fraction (x : K) :
-    ∃ (a : A) (b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x := by
+    ∃ (a : A) (b : nonZeroDivisors A), IsRelPrime a b ∧ mk' K a b = x := by
   obtain ⟨⟨b, b_nonzero⟩, a, hab⟩ := exists_integer_multiple (nonZeroDivisors A) x
   obtain ⟨a', b', c', no_factor, rfl, rfl⟩ :=
     UniqueFactorizationMonoid.exists_reduced_factors' a b
@@ -59,7 +59,7 @@ noncomputable def den (x : K) : nonZeroDivisors A :=
   Classical.choose (Classical.choose_spec (exists_reduced_fraction A x))
 #align is_fraction_ring.denom IsFractionRing.den
 
-theorem num_den_reduced (x : K) {d} : d ∣ num A x → d ∣ den A x → IsUnit d :=
+theorem num_den_reduced (x : K) : IsRelPrime (num A x) (den A x) :=
   (Classical.choose_spec (Classical.choose_spec (exists_reduced_fraction A x))).1
 #align is_fraction_ring.num_denom_reduced IsFractionRing.num_den_reduced
 

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).

@@ -93,7 +93,7 @@ theorem num_mul_den_eq_num_mul_den_iff_eq {x y : K} :
 #align is_fraction_ring.num_mul_denom_eq_num_mul_denom_iff_eq IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq
 
 theorem eq_zero_of_num_eq_zero {x : K} (h : num A x = 0) : x = 0 :=
-  num_mul_den_eq_num_iff_eq'.mp (by rw [MulZeroClass.zero_mul, h, RingHom.map_zero])
+  num_mul_den_eq_num_iff_eq'.mp (by rw [zero_mul, h, RingHom.map_zero])
 #align is_fraction_ring.eq_zero_of_num_eq_zero IsFractionRing.eq_zero_of_num_eq_zero
 
 theorem isInteger_of_isUnit_den {x : K} (h : IsUnit (den A x : A)) : IsInteger A x := by

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

This has nice performance benefits.

@@ -22,9 +22,9 @@ commutative ring, field of fractions
 -/
 
 
-variable {R : Type _} [CommRing R] (M : Submonoid R) {S : Type _} [CommRing S]
+variable {R : Type*} [CommRing R] (M : Submonoid R) {S : Type*} [CommRing S]
 
-variable [Algebra R S] {P : Type _} [CommRing P]
+variable [Algebra R S] {P : Type*} [CommRing P]
 
 namespace IsFractionRing
 
@@ -32,9 +32,9 @@ open IsLocalization
 
 section NumDen
 
-variable (A : Type _) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
+variable (A : Type*) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 
-variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
+variable {K : Type*} [Field K] [Algebra A K] [IsFractionRing A K]
 
 theorem exists_reduced_fraction (x : K) :
     ∃ (a : A) (b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x := by

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.num_denom
-! leanprover-community/mathlib commit 831c494092374cfe9f50591ed0ac81a25efc5b86
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Localization.FractionRing
 import Mathlib.RingTheory.Localization.Integer
 import Mathlib.RingTheory.UniqueFactorizationDomain
 
+#align_import ring_theory.localization.num_denom from "leanprover-community/mathlib"@"831c494092374cfe9f50591ed0ac81a25efc5b86"
+
 /-!
 # Numerator and denominator in a localization
 

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

@@ -40,7 +40,7 @@ variable (A : Type _) [CommRing A] [IsDomain A] [UniqueFactorizationMonoid A]
 variable {K : Type _} [Field K] [Algebra A K] [IsFractionRing A K]
 
 theorem exists_reduced_fraction (x : K) :
-    ∃ (a : A)(b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x := by
+    ∃ (a : A) (b : nonZeroDivisors A), (∀ {d}, d ∣ a → d ∣ b → IsUnit d) ∧ mk' K a b = x := by
   obtain ⟨⟨b, b_nonzero⟩, a, hab⟩ := exists_integer_multiple (nonZeroDivisors A) x
   obtain ⟨a', b', c', no_factor, rfl, rfl⟩ :=
     UniqueFactorizationMonoid.exists_reduced_factors' a b

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