linear_algebra.free_module.ideal_quotient

(last sync)

feat(linear_algebra/free_module/ideal_quotient): prove dimension of quotient by ideal equals degree of norm of generator (#19121)

Also refactor file into namespace ideal.

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

Diff

@@ -22,17 +22,20 @@ import linear_algebra.quotient_pi
 
 -/
 
-open_locale big_operators direct_sum
+namespace ideal
 
-variables {ι R S : Type*} [comm_ring R] [comm_ring S] [algebra R S]
-variables [is_domain R] [is_principal_ideal_ring R] [is_domain S] [fintype ι]
+open_locale big_operators direct_sum polynomial
+
+variables {R S ι : Type*} [comm_ring R] [comm_ring S] [algebra R S]
+variables [is_domain R] [is_principal_ideal_ring R] [is_domain S] [finite ι]
 
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
 -/
-noncomputable def ideal.quotient_equiv_pi_span
+noncomputable def quotient_equiv_pi_span
   (I : ideal S) (b : basis ι R S) (hI : I ≠ ⊥) :
-  (S ⧸ I) ≃ₗ[R] Π i, (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R)) :=
+  (S ⧸ I) ≃ₗ[R] Π i, (R ⧸ span ({I.smith_coeffs b hI i} : set R)) :=
 begin
+  haveI := fintype.of_finite ι,
   -- Choose `e : S ≃ₗ I` and a basis `b'` for `S` that turns the map
   -- `f := ((submodule.subtype I).restrict_scalars R).comp e` into a diagonal matrix:
   -- there is an `a : ι → ℤ` such that `f (b' i) = a i • b' i`.
@@ -57,10 +60,10 @@ begin
 
   -- Now we map everything through the linear equiv `S ≃ₗ (ι → R)`,
   -- which maps `I` to `I' := Π i, a i ℤ`.
-  let I' : submodule R (ι → R) := submodule.pi set.univ (λ i, ideal.span ({a i} : set R)),
+  let I' : submodule R (ι → R) := submodule.pi set.univ (λ i, span ({a i} : set R)),
   have : submodule.map (b'.equiv_fun : S →ₗ[R] (ι → R)) (I.restrict_scalars R) = I',
   { ext x,
-    simp only [submodule.mem_map, submodule.mem_pi, ideal.mem_span_singleton, set.mem_univ,
+    simp only [submodule.mem_map, submodule.mem_pi, mem_span_singleton, set.mem_univ,
                submodule.restrict_scalars_mem, mem_I_iff, smul_eq_mul, forall_true_left,
                linear_equiv.coe_coe, basis.equiv_fun_apply],
     split,
@@ -73,18 +76,18 @@ begin
   refine (submodule.quotient.equiv (I.restrict_scalars R) I' b'.equiv_fun this).trans _,
   any_goals { apply ring_hom.id }, any_goals { apply_instance },
   classical,
-  let := submodule.quotient_pi (show Π i, submodule R R, from λ i, ideal.span ({a i} : set R)),
+  let := submodule.quotient_pi (show Π i, submodule R R, from λ i, span ({a i} : set R)),
   exact this
 end
 
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of
 `zmod`. -/
-noncomputable def ideal.quotient_equiv_pi_zmod
+noncomputable def quotient_equiv_pi_zmod
   (I : ideal S) (b : basis ι ℤ S) (hI : I ≠ ⊥) :
   (S ⧸ I) ≃+ Π i, (zmod (I.smith_coeffs b hI i).nat_abs) :=
 let a := I.smith_coeffs b hI,
     e := I.quotient_equiv_pi_span b hI,
-    e' : (Π (i : ι), (ℤ ⧸ ideal.span ({a i} : set ℤ))) ≃+ Π (i : ι), zmod (a i).nat_abs :=
+    e' : (Π (i : ι), (ℤ ⧸ span ({a i} : set ℤ))) ≃+ Π (i : ι), zmod (a i).nat_abs :=
   add_equiv.Pi_congr_right (λ i, ↑(int.quotient_span_equiv_zmod (a i)))
 in (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : (S ⧸ I ≃+ _)).trans e'
 
@@ -93,14 +96,14 @@ in (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : (S ⧸ I ≃+ _)).trans e'
 Can't be an instance because of the side condition `I ≠ ⊥`, and more importantly,
 because the choice of `fintype` instance is non-canonical.
 -/
-noncomputable def ideal.fintype_quotient_of_free_of_ne_bot [module.free ℤ S] [module.finite ℤ S]
+noncomputable def fintype_quotient_of_free_of_ne_bot [module.free ℤ S] [module.finite ℤ S]
   (I : ideal S) (hI : I ≠ ⊥) :
   fintype (S ⧸ I) :=
 let b := module.free.choose_basis ℤ S,
     a := I.smith_coeffs b hI,
     e := I.quotient_equiv_pi_zmod b hI
 in by haveI : ∀ i, ne_zero (a i).nat_abs :=
-    (λ i, ⟨int.nat_abs_ne_zero_of_ne_zero (ideal.smith_coeffs_ne_zero b I hI i)⟩); classical;
+    (λ i, ⟨int.nat_abs_ne_zero_of_ne_zero (smith_coeffs_ne_zero b I hI i)⟩); classical;
   exact fintype.of_equiv (Π i, zmod (a i).nat_abs) e.symm
 
 variables (F : Type*) [comm_ring F] [algebra F R] [algebra F S] [is_scalar_tower F R S]
@@ -108,9 +111,10 @@ variables (F : Type*) [comm_ring F] [algebra F R] [algebra F S] [is_scalar_tower
 
 /-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules
   (quotients by the ideals generated by Smith coefficients of `I`). -/
-noncomputable def ideal.quotient_equiv_direct_sum :
-  (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R) :=
+noncomputable def quotient_equiv_direct_sum :
+  (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ span ({I.smith_coeffs b hI i} : set R) :=
 begin
+  haveI := fintype.of_finite ι,
   apply ((I.quotient_equiv_pi_span b _).restrict_scalars F).trans
     (direct_sum.linear_equiv_fun_on_fintype _ _ _).symm,
   exact linear_map.is_scalar_tower.compatible_smul
@@ -118,13 +122,15 @@ begin
   -- even after `change linear_map.compatible_smul _ (Π i, R ⧸ span _) F R`
 end
 
-lemma ideal.finrank_quotient_eq_sum [nontrivial F]
-  [∀ i, module.free F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R))]
-  [∀ i, module.finite F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R))] :
+lemma finrank_quotient_eq_sum {ι} [fintype ι] (b : basis ι R S) [nontrivial F]
+  [∀ i, module.free F (R ⧸ span ({I.smith_coeffs b hI i} : set R))]
+  [∀ i, module.finite F (R ⧸ span ({I.smith_coeffs b hI i} : set R))] :
   finite_dimensional.finrank F (S ⧸ I)
-    = ∑ i, finite_dimensional.finrank F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R)) :=
+    = ∑ i, finite_dimensional.finrank F (R ⧸ span ({I.smith_coeffs b hI i} : set R)) :=
 begin
-  rw [linear_equiv.finrank_eq $ ideal.quotient_equiv_direct_sum F b hI,
+  rw [linear_equiv.finrank_eq $ quotient_equiv_direct_sum F b hI,
       finite_dimensional.finrank_direct_sum]
   -- slow, and dot notation doesn't work
 end
+
+end ideal

feat(linear_algebra/free_module/ideal_quotient): add ideal.finrank_quotient_eq_sum (#19084)

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

Diff

@@ -5,8 +5,9 @@ Authors: Anne Baanen
 -/
 
 import data.zmod.quotient
-import linear_algebra.free_module.finite.basic
+import linear_algebra.free_module.finite.rank
 import linear_algebra.free_module.pid
+import linear_algebra.free_module.strong_rank_condition
 import linear_algebra.quotient_pi
 
 /-! # Ideals in free modules over PIDs
@@ -21,7 +22,7 @@ import linear_algebra.quotient_pi
 
 -/
 
-open_locale big_operators
+open_locale big_operators direct_sum
 
 variables {ι R S : Type*} [comm_ring R] [comm_ring S] [algebra R S]
 variables [is_domain R] [is_principal_ideal_ring R] [is_domain S] [fintype ι]
@@ -101,3 +102,29 @@ let b := module.free.choose_basis ℤ S,
 in by haveI : ∀ i, ne_zero (a i).nat_abs :=
     (λ i, ⟨int.nat_abs_ne_zero_of_ne_zero (ideal.smith_coeffs_ne_zero b I hI i)⟩); classical;
   exact fintype.of_equiv (Π i, zmod (a i).nat_abs) e.symm
+
+variables (F : Type*) [comm_ring F] [algebra F R] [algebra F S] [is_scalar_tower F R S]
+  (b : basis ι R S) {I : ideal S} (hI : I ≠ ⊥)
+
+/-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules
+  (quotients by the ideals generated by Smith coefficients of `I`). -/
+noncomputable def ideal.quotient_equiv_direct_sum :
+  (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R) :=
+begin
+  apply ((I.quotient_equiv_pi_span b _).restrict_scalars F).trans
+    (direct_sum.linear_equiv_fun_on_fintype _ _ _).symm,
+  exact linear_map.is_scalar_tower.compatible_smul
+  -- why doesn't it automatically apply?
+  -- even after `change linear_map.compatible_smul _ (Π i, R ⧸ span _) F R`
+end
+
+lemma ideal.finrank_quotient_eq_sum [nontrivial F]
+  [∀ i, module.free F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R))]
+  [∀ i, module.finite F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R))] :
+  finite_dimensional.finrank F (S ⧸ I)
+    = ∑ i, finite_dimensional.finrank F (R ⧸ ideal.span ({I.smith_coeffs b hI i} : set R)) :=
+begin
+  rw [linear_equiv.finrank_eq $ ideal.quotient_equiv_direct_sum F b hI,
+      finite_dimensional.finrank_direct_sum]
+  -- slow, and dot notation doesn't work
+end

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Data.Zmod.Quotient
+import Data.ZMod.Quotient
 import LinearAlgebra.FreeModule.Finite.Rank
-import LinearAlgebra.FreeModule.Pid
+import LinearAlgebra.FreeModule.PID
 import LinearAlgebra.FreeModule.StrongRankCondition
 import LinearAlgebra.QuotientPi

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -81,6 +81,8 @@ noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I 
   refine' (Submodule.Quotient.equiv (I.restrict_scalars R) I' b'.equiv_fun this).trans _
   any_goals apply RingHom.id; any_goals infer_instance
   classical
+  let this.1 := Submodule.quotientPi (show ∀ i, Submodule R R from fun i => span ({a i} : Set R))
+  exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 -/
 
@@ -111,7 +113,7 @@ noncomputable def fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finit
   let e := I.quotientEquivPiZMod b hI
   haveI : ∀ i, NeZero (a i).natAbs := fun i =>
         ⟨Int.natAbs_ne_zero_of_ne_zero (smith_coeffs_ne_zero b I hI i)⟩ <;>
-      classical <;>
+      classical skip <;>
     exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -81,8 +81,6 @@ noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I 
   refine' (Submodule.Quotient.equiv (I.restrict_scalars R) I' b'.equiv_fun this).trans _
   any_goals apply RingHom.id; any_goals infer_instance
   classical
-  let this.1 := Submodule.quotientPi (show ∀ i, Submodule R R from fun i => span ({a i} : Set R))
-  exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 -/
 
@@ -113,7 +111,7 @@ noncomputable def fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finit
   let e := I.quotientEquivPiZMod b hI
   haveI : ∀ i, NeZero (a i).natAbs := fun i =>
         ⟨Int.natAbs_ne_zero_of_ne_zero (smith_coeffs_ne_zero b I hI i)⟩ <;>
-      classical skip <;>
+      classical <;>
     exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathbin.Data.Zmod.Quotient
-import Mathbin.LinearAlgebra.FreeModule.Finite.Rank
-import Mathbin.LinearAlgebra.FreeModule.Pid
-import Mathbin.LinearAlgebra.FreeModule.StrongRankCondition
-import Mathbin.LinearAlgebra.QuotientPi
+import Data.Zmod.Quotient
+import LinearAlgebra.FreeModule.Finite.Rank
+import LinearAlgebra.FreeModule.Pid
+import LinearAlgebra.FreeModule.StrongRankCondition
+import LinearAlgebra.QuotientPi
 
 #align_import linear_algebra.free_module.ideal_quotient from "leanprover-community/mathlib"@"90b0d53ee6ffa910e5c2a977ce7e2fc704647974"

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -57,7 +57,7 @@ noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I 
     have : ∀ (c : ι → R) (i), b'.repr (∑ j : ι, c j • a j • b' j) i = a i * c i :=
       by
       intro c i
-      simp only [← MulAction.mul_smul, b'.repr_sum_self, mul_comm]
+      simp only [← MulAction.hMul_smul, b'.repr_sum_self, mul_comm]
     constructor
     · rintro ⟨c, rfl⟩ i; exact ⟨c i, this c i⟩
     · rintro ha

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.free_module.ideal_quotient
-! leanprover-community/mathlib commit 90b0d53ee6ffa910e5c2a977ce7e2fc704647974
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Zmod.Quotient
 import Mathbin.LinearAlgebra.FreeModule.Finite.Rank
@@ -14,6 +9,8 @@ import Mathbin.LinearAlgebra.FreeModule.Pid
 import Mathbin.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathbin.LinearAlgebra.QuotientPi
 
+#align_import linear_algebra.free_module.ideal_quotient from "leanprover-community/mathlib"@"90b0d53ee6ffa910e5c2a977ce7e2fc704647974"
+
 /-! # Ideals in free modules over PIDs
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -35,6 +35,7 @@ variable {R S ι : Type _} [CommRing R] [CommRing S] [Algebra R S]
 
 variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Finite ι]
 
+#print Ideal.quotientEquivPiSpan /-
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
 -/
 noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I ≠ ⊥) :
@@ -86,7 +87,9 @@ noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I 
   let this.1 := Submodule.quotientPi (show ∀ i, Submodule R R from fun i => span ({a i} : Set R))
   exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
+-/
 
+#print Ideal.quotientEquivPiZMod /-
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of
 `zmod`. -/
 noncomputable def quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
@@ -97,7 +100,9 @@ noncomputable def quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I
     AddEquiv.piCongrRight fun i => ↑(Int.quotientSpanEquivZMod (a i))
   (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : S ⧸ I ≃+ _).trans e'
 #align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZMod
+-/
 
+#print Ideal.fintypeQuotientOfFreeOfNeBot /-
 /-- A nonzero ideal over a free finite extension of `ℤ` has a finite quotient.
 
 Can't be an instance because of the side condition `I ≠ ⊥`, and more importantly,
@@ -114,10 +119,12 @@ noncomputable def fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finit
       classical skip <;>
     exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
+-/
 
 variable (F : Type _) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F R S]
   (b : Basis ι R S) {I : Ideal S} (hI : I ≠ ⊥)
 
+#print Ideal.quotientEquivDirectSum /-
 /-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules
   (quotients by the ideals generated by Smith coefficients of `I`). -/
 noncomputable def quotientEquivDirectSum :
@@ -129,7 +136,9 @@ noncomputable def quotientEquivDirectSum :
       (DirectSum.linearEquivFunOnFintype _ _ _).symm
   exact LinearMap.IsScalarTower.compatibleSMul
 #align ideal.quotient_equiv_direct_sum Ideal.quotientEquivDirectSum
+-/
 
+#print Ideal.finrank_quotient_eq_sum /-
 -- why doesn't it automatically apply?
 -- even after `change linear_map.compatible_smul _ (Π i, R ⧸ span _) F R`
 theorem finrank_quotient_eq_sum {ι} [Fintype ι] (b : Basis ι R S) [Nontrivial F]
@@ -141,6 +150,7 @@ theorem finrank_quotient_eq_sum {ι} [Fintype ι] (b : Basis ι R S) [Nontrivial
   rw [LinearEquiv.finrank_eq <| quotient_equiv_direct_sum F b hI,
     FiniteDimensional.finrank_directSum]
 #align ideal.finrank_quotient_eq_sum Ideal.finrank_quotient_eq_sum
+-/
 
 -- slow, and dot notation doesn't work
 end Ideal

bump to nightly-2023-06-11-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

6960a941

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.ideal_quotient
-! leanprover-community/mathlib commit d87199d51218d36a0a42c66c82d147b5a7ff87b3
+! leanprover-community/mathlib commit 90b0d53ee6ffa910e5c2a977ce7e2fc704647974
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -27,17 +27,20 @@ import Mathbin.LinearAlgebra.QuotientPi
 -/
 
 
-open scoped BigOperators DirectSum
+namespace Ideal
 
-variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
+open scoped BigOperators DirectSum Polynomial
 
-variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Fintype ι]
+variable {R S ι : Type _} [CommRing R] [CommRing S] [Algebra R S]
+
+variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Finite ι]
 
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
 -/
-noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I ≠ ⊥) :
-    (S ⧸ I) ≃ₗ[R] ∀ i, R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R) :=
+noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I ≠ ⊥) :
+    (S ⧸ I) ≃ₗ[R] ∀ i, R ⧸ span ({I.smithCoeffs b hI i} : Set R) :=
   by
+  haveI := Fintype.ofFinite ι
   -- Choose `e : S ≃ₗ I` and a basis `b'` for `S` that turns the map
   -- `f := ((submodule.subtype I).restrict_scalars R).comp e` into a diagonal matrix:
   -- there is an `a : ι → ℤ` such that `f (b' i) = a i • b' i`.
@@ -63,11 +66,11 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
       choose c hc using ha; exact ⟨c, b'.ext_elem fun i => trans (hc i) (this c i).symm⟩
   -- Now we map everything through the linear equiv `S ≃ₗ (ι → R)`,
   -- which maps `I` to `I' := Π i, a i ℤ`.
-  let I' : Submodule R (ι → R) := Submodule.pi Set.univ fun i => Ideal.span ({a i} : Set R)
+  let I' : Submodule R (ι → R) := Submodule.pi Set.univ fun i => span ({a i} : Set R)
   have : Submodule.map (b'.equiv_fun : S →ₗ[R] ι → R) (I.restrict_scalars R) = I' :=
     by
     ext x
-    simp only [Submodule.mem_map, Submodule.mem_pi, Ideal.mem_span_singleton, Set.mem_univ,
+    simp only [Submodule.mem_map, Submodule.mem_pi, mem_span_singleton, Set.mem_univ,
       Submodule.restrictScalars_mem, mem_I_iff, smul_eq_mul, forall_true_left, LinearEquiv.coe_coe,
       Basis.equivFun_apply]
     constructor
@@ -80,18 +83,17 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
   refine' (Submodule.Quotient.equiv (I.restrict_scalars R) I' b'.equiv_fun this).trans _
   any_goals apply RingHom.id; any_goals infer_instance
   classical
-  let this.1 :=
-    Submodule.quotientPi (show ∀ i, Submodule R R from fun i => Ideal.span ({a i} : Set R))
+  let this.1 := Submodule.quotientPi (show ∀ i, Submodule R R from fun i => span ({a i} : Set R))
   exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of
 `zmod`. -/
-noncomputable def Ideal.quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
+noncomputable def quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
     S ⧸ I ≃+ ∀ i, ZMod (I.smithCoeffs b hI i).natAbs :=
   let a := I.smithCoeffs b hI
   let e := I.quotientEquivPiSpan b hI
-  let e' : (∀ i : ι, ℤ ⧸ Ideal.span ({a i} : Set ℤ)) ≃+ ∀ i : ι, ZMod (a i).natAbs :=
+  let e' : (∀ i : ι, ℤ ⧸ span ({a i} : Set ℤ)) ≃+ ∀ i : ι, ZMod (a i).natAbs :=
     AddEquiv.piCongrRight fun i => ↑(Int.quotientSpanEquivZMod (a i))
   (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : S ⧸ I ≃+ _).trans e'
 #align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZMod
@@ -101,14 +103,14 @@ noncomputable def Ideal.quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (
 Can't be an instance because of the side condition `I ≠ ⊥`, and more importantly,
 because the choice of `fintype` instance is non-canonical.
 -/
-noncomputable def Ideal.fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finite ℤ S]
-    (I : Ideal S) (hI : I ≠ ⊥) : Fintype (S ⧸ I) :=
+noncomputable def fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finite ℤ S] (I : Ideal S)
+    (hI : I ≠ ⊥) : Fintype (S ⧸ I) :=
   by
   let b := Module.Free.chooseBasis ℤ S
   let a := I.smithCoeffs b hI
   let e := I.quotientEquivPiZMod b hI
   haveI : ∀ i, NeZero (a i).natAbs := fun i =>
-        ⟨Int.natAbs_ne_zero_of_ne_zero (Ideal.smithCoeffs_ne_zero b I hI i)⟩ <;>
+        ⟨Int.natAbs_ne_zero_of_ne_zero (smith_coeffs_ne_zero b I hI i)⟩ <;>
       classical skip <;>
     exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
@@ -118,9 +120,10 @@ variable (F : Type _) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F
 
 /-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules
   (quotients by the ideals generated by Smith coefficients of `I`). -/
-noncomputable def Ideal.quotientEquivDirectSum :
-    (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R) :=
+noncomputable def quotientEquivDirectSum :
+    (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ span ({I.smithCoeffs b hI i} : Set R) :=
   by
+  haveI := Fintype.ofFinite ι
   apply
     ((I.quotient_equiv_pi_span b _).restrictScalars F).trans
       (DirectSum.linearEquivFunOnFintype _ _ _).symm
@@ -129,14 +132,16 @@ noncomputable def Ideal.quotientEquivDirectSum :
 
 -- why doesn't it automatically apply?
 -- even after `change linear_map.compatible_smul _ (Π i, R ⧸ span _) F R`
-theorem Ideal.finrank_quotient_eq_sum [Nontrivial F]
-    [∀ i, Module.Free F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))]
-    [∀ i, Module.Finite F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))] :
+theorem finrank_quotient_eq_sum {ι} [Fintype ι] (b : Basis ι R S) [Nontrivial F]
+    [∀ i, Module.Free F (R ⧸ span ({I.smithCoeffs b hI i} : Set R))]
+    [∀ i, Module.Finite F (R ⧸ span ({I.smithCoeffs b hI i} : Set R))] :
     FiniteDimensional.finrank F (S ⧸ I) =
-      ∑ i, FiniteDimensional.finrank F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R)) :=
+      ∑ i, FiniteDimensional.finrank F (R ⧸ span ({I.smithCoeffs b hI i} : Set R)) :=
   by
-  rw [LinearEquiv.finrank_eq <| Ideal.quotientEquivDirectSum F b hI,
+  rw [LinearEquiv.finrank_eq <| quotient_equiv_direct_sum F b hI,
     FiniteDimensional.finrank_directSum]
 #align ideal.finrank_quotient_eq_sum Ideal.finrank_quotient_eq_sum
 
 -- slow, and dot notation doesn't work
+end Ideal
+

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -80,7 +80,7 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
   refine' (Submodule.Quotient.equiv (I.restrict_scalars R) I' b'.equiv_fun this).trans _
   any_goals apply RingHom.id; any_goals infer_instance
   classical
-  let this :=
+  let this.1 :=
     Submodule.quotientPi (show ∀ i, Submodule R R from fun i => Ideal.span ({a i} : Set R))
   exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -80,9 +80,9 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
   refine' (Submodule.Quotient.equiv (I.restrict_scalars R) I' b'.equiv_fun this).trans _
   any_goals apply RingHom.id; any_goals infer_instance
   classical
-    let this :=
-      Submodule.quotientPi (show ∀ i, Submodule R R from fun i => Ideal.span ({a i} : Set R))
-    exact this
+  let this :=
+    Submodule.quotientPi (show ∀ i, Submodule R R from fun i => Ideal.span ({a i} : Set R))
+  exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of

bump to nightly-2023-05-29-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/88a563b158f59f2983cfad685664da95502e8cdd

d0f5dd0a

Diff

@@ -4,13 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.ideal_quotient
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
+! leanprover-community/mathlib commit d87199d51218d36a0a42c66c82d147b5a7ff87b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Zmod.Quotient
-import Mathbin.LinearAlgebra.FreeModule.Finite.Basic
+import Mathbin.LinearAlgebra.FreeModule.Finite.Rank
 import Mathbin.LinearAlgebra.FreeModule.Pid
+import Mathbin.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathbin.LinearAlgebra.QuotientPi
 
 /-! # Ideals in free modules over PIDs
@@ -26,7 +27,7 @@ import Mathbin.LinearAlgebra.QuotientPi
 -/
 
 
-open scoped BigOperators
+open scoped BigOperators DirectSum
 
 variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
 
@@ -112,3 +113,30 @@ noncomputable def Ideal.fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module
     exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
 
+variable (F : Type _) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F R S]
+  (b : Basis ι R S) {I : Ideal S} (hI : I ≠ ⊥)
+
+/-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules
+  (quotients by the ideals generated by Smith coefficients of `I`). -/
+noncomputable def Ideal.quotientEquivDirectSum :
+    (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R) :=
+  by
+  apply
+    ((I.quotient_equiv_pi_span b _).restrictScalars F).trans
+      (DirectSum.linearEquivFunOnFintype _ _ _).symm
+  exact LinearMap.IsScalarTower.compatibleSMul
+#align ideal.quotient_equiv_direct_sum Ideal.quotientEquivDirectSum
+
+-- why doesn't it automatically apply?
+-- even after `change linear_map.compatible_smul _ (Π i, R ⧸ span _) F R`
+theorem Ideal.finrank_quotient_eq_sum [Nontrivial F]
+    [∀ i, Module.Free F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))]
+    [∀ i, Module.Finite F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))] :
+    FiniteDimensional.finrank F (S ⧸ I) =
+      ∑ i, FiniteDimensional.finrank F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R)) :=
+  by
+  rw [LinearEquiv.finrank_eq <| Ideal.quotientEquivDirectSum F b hI,
+    FiniteDimensional.finrank_directSum]
+#align ideal.finrank_quotient_eq_sum Ideal.finrank_quotient_eq_sum
+
+-- slow, and dot notation doesn't work

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ import Mathbin.LinearAlgebra.QuotientPi
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -32,9 +32,6 @@ variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
 
 variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Fintype ι]
 
-/- warning: ideal.quotient_equiv_pi_span -> Ideal.quotientEquivPiSpan is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpanₓ'. -/
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
 -/
 noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I ≠ ⊥) :
@@ -87,9 +84,6 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
     exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 
-/- warning: ideal.quotient_equiv_pi_zmod -> Ideal.quotientEquivPiZMod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZModₓ'. -/
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of
 `zmod`. -/
 noncomputable def Ideal.quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
@@ -101,12 +95,6 @@ noncomputable def Ideal.quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (
   (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : S ⧸ I ≃+ _).trans e'
 #align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZMod
 
-/- warning: ideal.fintype_quotient_of_free_of_ne_bot -> Ideal.fintypeQuotientOfFreeOfNeBot is a dubious translation:
-lean 3 declaration is
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_8 : Module.Free.{0, u1} Int S Int.semiring (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))] [_inst_9 : Module.Finite.{0, u1} Int S Int.semiring (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))] (I : Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))), (Ne.{succ u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) I (Bot.bot.{u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Submodule.hasBot.{u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) -> (Fintype.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ideal.hasQuotient.{u1} S _inst_2) I))
-but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_8 : Module.Free.{0, u1} Int S Int.instSemiringInt (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (Ring.toAddCommGroup.{u1} S (CommRing.toRing.{u1} S _inst_2)))] [_inst_9 : Module.Finite.{0, u1} Int S Int.instSemiringInt (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (Ring.toAddCommGroup.{u1} S (CommRing.toRing.{u1} S _inst_2)))] (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))), (Ne.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) I (Bot.bot.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Submodule.instBotSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) -> (Fintype.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) I))
-Case conversion may be inaccurate. Consider using '#align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBotₓ'. -/
 /-- A nonzero ideal over a free finite extension of `ℤ` has a finite quotient.
 
 Can't be an instance because of the side condition `I ≠ ⊥`, and more importantly,

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -50,23 +50,19 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
   let e : S ≃ₗ[R] I := b'.equiv ab (Equiv.refl _)
   let f : S →ₗ[R] S := (I.subtype.restrict_scalars R).comp (e : S →ₗ[R] I)
   let f_apply : ∀ x, f x = b'.equiv ab (Equiv.refl _) x := fun x => rfl
-  have ha : ∀ i, f (b' i) = a i • b' i := by
-    intro i
+  have ha : ∀ i, f (b' i) = a i • b' i := by intro i;
     rw [f_apply, b'.equiv_apply, Equiv.refl_apply, ab_eq]
   have mem_I_iff : ∀ x, x ∈ I ↔ ∀ i, a i ∣ b'.repr x i :=
     by
-    intro x
-    simp_rw [ab.mem_ideal_iff', ab_eq]
+    intro x; simp_rw [ab.mem_ideal_iff', ab_eq]
     have : ∀ (c : ι → R) (i), b'.repr (∑ j : ι, c j • a j • b' j) i = a i * c i :=
       by
       intro c i
       simp only [← MulAction.mul_smul, b'.repr_sum_self, mul_comm]
     constructor
-    · rintro ⟨c, rfl⟩ i
-      exact ⟨c i, this c i⟩
+    · rintro ⟨c, rfl⟩ i; exact ⟨c i, this c i⟩
     · rintro ha
-      choose c hc using ha
-      exact ⟨c, b'.ext_elem fun i => trans (hc i) (this c i).symm⟩
+      choose c hc using ha; exact ⟨c, b'.ext_elem fun i => trans (hc i) (this c i).symm⟩
   -- Now we map everything through the linear equiv `S ≃ₗ (ι → R)`,
   -- which maps `I` to `I' := Π i, a i ℤ`.
   let I' : Submodule R (ι → R) := Submodule.pi Set.univ fun i => Ideal.span ({a i} : Set R)
@@ -77,17 +73,14 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
       Submodule.restrictScalars_mem, mem_I_iff, smul_eq_mul, forall_true_left, LinearEquiv.coe_coe,
       Basis.equivFun_apply]
     constructor
-    · rintro ⟨y, hy, rfl⟩ i
-      exact hy i
+    · rintro ⟨y, hy, rfl⟩ i; exact hy i
     · rintro hdvd
       refine' ⟨∑ i, x i • b' i, fun i => _, _⟩ <;> rwa [b'.repr_sum_self]
       · exact hdvd i
   refine' ((Submodule.Quotient.restrictScalarsEquiv R I).restrictScalars R).symm.trans _
-  any_goals apply RingHom.id
-  any_goals infer_instance
+  any_goals apply RingHom.id; any_goals infer_instance
   refine' (Submodule.Quotient.equiv (I.restrict_scalars R) I' b'.equiv_fun this).trans _
-  any_goals apply RingHom.id
-  any_goals infer_instance
+  any_goals apply RingHom.id; any_goals infer_instance
   classical
     let this :=
       Submodule.quotientPi (show ∀ i, Submodule R R from fun i => Ideal.span ({a i} : Set R))

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.ideal_quotient
-! leanprover-community/mathlib commit 6623e6af705e97002a9054c1c05a980180276fc1
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.QuotientPi
 
 /-! # Ideals in free modules over PIDs
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main results
 
  - `ideal.quotient_equiv_pi_span`: `S ⧸ I`, if `S` is finite free as a module over a PID `R`,
@@ -30,10 +33,7 @@ variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
 variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Fintype ι]
 
 /- warning: ideal.quotient_equiv_pi_span -> Ideal.quotientEquivPiSpan is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_4 : IsDomain.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] [_inst_5 : IsPrincipalIdealRing.{u2} R (CommRing.toRing.{u2} R _inst_1)] [_inst_6 : IsDomain.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (b : Basis.{u1, u2, u3} ι R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} S (NonUnitalNonAssocRing.toAddCommGroup.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3)) (hI : Ne.{succ u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) I (Bot.bot.{u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (Submodule.hasBot.{u3, u3} S S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))), LinearEquiv.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (Ideal.quotientEquivPiSpan._proof_1.{u2} R _inst_1) (Ideal.quotientEquivPiSpan._proof_2.{u2} R _inst_1) (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (Ideal.hasQuotient.{u3} S _inst_2) I) (forall (i : ι), HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (Ideal.hasQuotient.{u3} S _inst_2) I) (Submodule.Quotient.addCommGroup.{u3, u3} S S (CommRing.toRing.{u3} S _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) I)) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))))))) (Submodule.Quotient.module'.{u3, u3, u2} S S (CommRing.toRing.{u3} S _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (SMulZeroClass.toHasSmul.{u2, u3} R S (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R S (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R S (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (Module.toMulActionWithZero.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3) (Ideal.quotientEquivPiSpan._proof_3.{u2, u3} R S _inst_1 _inst_2 _inst_3) I) (Algebra.toModule.{u2, max u1 u2} R (forall (i : ι), HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Pi.semiring.{u1, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (fun (i : ι) => Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))) (Pi.algebra.{u1, u2, u2} ι R (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toCommSemiring.{u2} R _inst_1) (fun (i : ι) => Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))) (fun (i : ι) => Ideal.Quotient.algebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_1 (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_4 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_5 : IsPrincipalIdealRing.{u2} R (CommRing.toRing.{u2} R _inst_1)] [_inst_6 : IsDomain.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (b : Basis.{u1, u2, u3} ι R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)) (hI : Ne.{succ u3} (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) I (Bot.bot.{u3} (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Submodule.instBotSubmodule.{u3, u3} S S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))))), LinearEquiv.{u2, u2, u3, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (forall (i : ι), HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (NonAssocRing.toNonUnitalNonAssocRing.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (Ring.toNonAssocRing.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (CommRing.toRing.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (Ideal.Quotient.commRing.{u3} S _inst_2 I)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))))))) (Submodule.Quotient.module'.{u3, u3, u2} S S (CommRing.toRing.{u3} S _inst_2) (Ring.toAddCommGroup.{u3} S (CommRing.toRing.{u3} S _inst_2)) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (IsScalarTower.right.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) I) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))))) (fun (i : ι) => Submodule.Quotient.module.{u2, u2} R R (CommRing.toRing.{u2} R _inst_1) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpanₓ'. -/
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
 -/
@@ -95,10 +95,7 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 
 /- warning: ideal.quotient_equiv_pi_zmod -> Ideal.quotientEquivPiZMod is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (b : Basis.{u1, 0, u2} ι Int S Int.semiring (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (AddCommGroup.intModule.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))) (hI : Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) I (Bot.bot.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.hasBot.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))), AddEquiv.{u2, u1} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (forall (i : ι), ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_1 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Distrib.toHasAdd.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (Ring.toDistrib.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (Pi.instAdd.{u1, 0} ι (fun (i : ι) => ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_2 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (fun (i : ι) => Distrib.toHasAdd.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Ring.toDistrib.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (CommRing.toRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (ZMod.commRing (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))))
-but is expected to have type
-  forall {ι : Type.{u1}} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (b : Basis.{u1, 0, u2} ι Int S Int.instSemiringInt (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (AddCommGroup.intModule.{u2} S (Ring.toAddCommGroup.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (hI : Ne.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) I (Bot.bot.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Submodule.instBotSubmodule.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))), AddEquiv.{u2, u1} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (forall (i : ι), ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Distrib.toAdd.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonUnitalNonAssocSemiring.toDistrib.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))))) (Pi.instAdd.{u1, 0} ι (fun (i : ι) => ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (fun (i : ι) => Distrib.toAdd.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Ring.toNonAssocRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (CommRing.toRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (ZMod.commRing (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZModₓ'. -/
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of
 `zmod`. -/

bump to nightly-2023-05-26-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

d59ee359

Diff

@@ -29,6 +29,12 @@ variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
 
 variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Fintype ι]
 
+/- warning: ideal.quotient_equiv_pi_span -> Ideal.quotientEquivPiSpan is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_4 : IsDomain.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))] [_inst_5 : IsPrincipalIdealRing.{u2} R (CommRing.toRing.{u2} R _inst_1)] [_inst_6 : IsDomain.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (b : Basis.{u1, u2, u3} ι R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} S (NonUnitalNonAssocRing.toAddCommGroup.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3)) (hI : Ne.{succ u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) I (Bot.bot.{u3} (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (Submodule.hasBot.{u3, u3} S S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))), LinearEquiv.{u2, u2, u3, max u1 u2} R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (Ideal.quotientEquivPiSpan._proof_1.{u2} R _inst_1) (Ideal.quotientEquivPiSpan._proof_2.{u2} R _inst_1) (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (Ideal.hasQuotient.{u3} S _inst_2) I) (forall (i : ι), HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (AddCommGroup.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) (Ideal.hasQuotient.{u3} S _inst_2) I) (Submodule.Quotient.addCommGroup.{u3, u3} S S (CommRing.toRing.{u3} S _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) I)) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocRing.toAddCommGroup.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))))))) (Submodule.Quotient.module'.{u3, u3, u2} S S (CommRing.toRing.{u3} S _inst_2) (NonUnitalNonAssocRing.toAddCommGroup.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (Semiring.toModule.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))) R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (SMulZeroClass.toHasSmul.{u2, u3} R S (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R S (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R S (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddZeroClass.toHasZero.{u3} S (AddMonoid.toAddZeroClass.{u3} S (AddCommMonoid.toAddMonoid.{u3} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)))))))) (Module.toMulActionWithZero.{u2, u3} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) _inst_3) (Ideal.quotientEquivPiSpan._proof_3.{u2, u3} R S _inst_1 _inst_2 _inst_3) I) (Algebra.toModule.{u2, max u1 u2} R (forall (i : ι), HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toCommSemiring.{u2} R _inst_1) (Pi.semiring.{u1, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (fun (i : ι) => Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))) (Pi.algebra.{u1, u2, u2} ι R (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toCommSemiring.{u2} R _inst_1) (fun (i : ι) => Ring.toSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Ideal.hasQuotient.{u2} R _inst_1) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))) (fun (i : ι) => Ideal.Quotient.algebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) _inst_1 (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ideal.span.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.hasSingleton.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_4 : IsDomain.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))] [_inst_5 : IsPrincipalIdealRing.{u2} R (CommRing.toRing.{u2} R _inst_1)] [_inst_6 : IsDomain.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (b : Basis.{u1, u2, u3} ι R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonUnitalNonAssocRing.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2))))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3)) (hI : Ne.{succ u3} (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) I (Bot.bot.{u3} (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Submodule.instBotSubmodule.{u3, u3} S S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))))) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)))))), LinearEquiv.{u2, u2, u3, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHomInvPair.ids.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (forall (i : ι), HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (NonAssocRing.toNonUnitalNonAssocRing.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (Ring.toNonAssocRing.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (CommRing.toRing.{u3} (HasQuotient.Quotient.{u3, u3} S (Ideal.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u3} S _inst_2) I) (Ideal.Quotient.commRing.{u3} S _inst_2 I)))))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))))))) (Submodule.Quotient.module'.{u3, u3, u2} S S (CommRing.toRing.{u3} S _inst_2) (Ring.toAddCommGroup.{u3} S (CommRing.toRing.{u3} S _inst_2)) (Semiring.toModule.{u3} S (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2))) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.toSMul.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) (IsScalarTower.right.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} S (CommRing.toCommSemiring.{u3} S _inst_2)) _inst_3) I) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} R _inst_1) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))) (Ideal.Quotient.commRing.{u2} R _inst_1 (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))))) (fun (i : ι) => Submodule.Quotient.module.{u2, u2} R R (CommRing.toRing.{u2} R _inst_1) (Ring.toAddCommGroup.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ideal.span.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Singleton.singleton.{u2, u2} R (Set.{u2} R) (Set.instSingletonSet.{u2} R) (Ideal.smithCoeffs.{u1, u2, u3} ι R _inst_1 _inst_4 _inst_5 S _inst_2 _inst_6 _inst_3 (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))
+Case conversion may be inaccurate. Consider using '#align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpanₓ'. -/
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
 -/
 noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I ≠ ⊥) :
@@ -88,17 +94,29 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
     exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 
+/- warning: ideal.quotient_equiv_pi_zmod -> Ideal.quotientEquivPiZMod is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (b : Basis.{u1, 0, u2} ι Int S Int.semiring (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (AddCommGroup.intModule.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2)))))) (hI : Ne.{succ u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) I (Bot.bot.{u2} (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Submodule.hasBot.{u2, u2} S S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2)))))), AddEquiv.{u2, u1} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (forall (i : ι), ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_1 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Distrib.toHasAdd.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (Ring.toDistrib.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_2))) (Ideal.hasQuotient.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I)))) (Pi.instAdd.{u1, 0} ι (fun (i : ι) => ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_2 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (fun (i : ι) => Distrib.toHasAdd.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Ring.toDistrib.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (CommRing.toRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (ZMod.commRing (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.commRing Ideal.quotientEquivPiZMod._proof_3 (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i)))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {S : Type.{u2}} [_inst_2 : CommRing.{u2} S] [_inst_6 : IsDomain.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))] [_inst_7 : Fintype.{u1} ι] (I : Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (b : Basis.{u1, 0, u2} ι Int S Int.instSemiringInt (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_2))))) (AddCommGroup.intModule.{u2} S (Ring.toAddCommGroup.{u2} S (CommRing.toRing.{u2} S _inst_2)))) (hI : Ne.{succ u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) I (Bot.bot.{u2} (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Submodule.instBotSubmodule.{u2, u2} S S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))))) (Semiring.toModule.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2)))))), AddEquiv.{u2, u1} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (forall (i : ι), ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Distrib.toAdd.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonUnitalNonAssocSemiring.toDistrib.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (NonAssocRing.toNonUnitalNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Ring.toNonAssocRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (CommRing.toRing.{u2} (HasQuotient.Quotient.{u2, u2} S (Ideal.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u2} S _inst_2) I) (Ideal.Quotient.commRing.{u2} S _inst_2 I))))))) (Pi.instAdd.{u1, 0} ι (fun (i : ι) => ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (fun (i : ι) => Distrib.toAdd.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (NonUnitalNonAssocSemiring.toDistrib.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (NonAssocRing.toNonUnitalNonAssocRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (Ring.toNonAssocRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (CommRing.toRing.{0} (ZMod (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))) (ZMod.commRing (Int.natAbs (Ideal.smithCoeffs.{u1, 0, u2} ι Int Int.instCommRingInt (LinearOrderedRing.isDomain.{0} Int (LinearOrderedCommRing.toLinearOrderedRing.{0} Int Int.linearOrderedCommRing)) (EuclideanDomain.to_principal_ideal_domain.{0} Int Int.euclideanDomain) S _inst_2 _inst_6 (algebraInt.{u2} S (CommRing.toRing.{u2} S _inst_2)) (Finite.of_fintype.{u1} ι _inst_7) b I hI i))))))))))
+Case conversion may be inaccurate. Consider using '#align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZModₓ'. -/
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of
 `zmod`. -/
-noncomputable def Ideal.quotientEquivPiZmod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
+noncomputable def Ideal.quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
     S ⧸ I ≃+ ∀ i, ZMod (I.smithCoeffs b hI i).natAbs :=
   let a := I.smithCoeffs b hI
   let e := I.quotientEquivPiSpan b hI
   let e' : (∀ i : ι, ℤ ⧸ Ideal.span ({a i} : Set ℤ)) ≃+ ∀ i : ι, ZMod (a i).natAbs :=
     AddEquiv.piCongrRight fun i => ↑(Int.quotientSpanEquivZMod (a i))
   (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : S ⧸ I ≃+ _).trans e'
-#align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZmod
+#align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZMod
 
+/- warning: ideal.fintype_quotient_of_free_of_ne_bot -> Ideal.fintypeQuotientOfFreeOfNeBot is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))] [_inst_8 : Module.Free.{0, u1} Int S Int.semiring (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))] [_inst_9 : Module.Finite.{0, u1} Int S Int.semiring (AddCommGroup.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (NonUnitalNonAssocRing.toAddCommGroup.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2)))))] (I : Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))), (Ne.{succ u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) I (Bot.bot.{u1} (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Submodule.hasBot.{u1, u1} S S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) -> (Fintype.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Ideal.hasQuotient.{u1} S _inst_2) I))
+but is expected to have type
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] [_inst_6 : IsDomain.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))] [_inst_8 : Module.Free.{0, u1} Int S Int.instSemiringInt (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (Ring.toAddCommGroup.{u1} S (CommRing.toRing.{u1} S _inst_2)))] [_inst_9 : Module.Finite.{0, u1} Int S Int.instSemiringInt (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (AddCommGroup.intModule.{u1} S (Ring.toAddCommGroup.{u1} S (CommRing.toRing.{u1} S _inst_2)))] (I : Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))), (Ne.{succ u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) I (Bot.bot.{u1} (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Submodule.instBotSubmodule.{u1, u1} S S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Semiring.toModule.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) -> (Fintype.{u1} (HasQuotient.Quotient.{u1, u1} S (Ideal.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} S _inst_2) I))
+Case conversion may be inaccurate. Consider using '#align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBotₓ'. -/
 /-- A nonzero ideal over a free finite extension of `ℤ` has a finite quotient.
 
 Can't be an instance because of the side condition `I ≠ ⊥`, and more importantly,
@@ -109,7 +127,7 @@ noncomputable def Ideal.fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module
   by
   let b := Module.Free.chooseBasis ℤ S
   let a := I.smithCoeffs b hI
-  let e := I.quotientEquivPiZmod b hI
+  let e := I.quotientEquivPiZMod b hI
   haveI : ∀ i, NeZero (a i).natAbs := fun i =>
         ⟨Int.natAbs_ne_zero_of_ne_zero (Ideal.smithCoeffs_ne_zero b I hI i)⟩ <;>
       classical skip <;>

bump to nightly-2023-05-25-16

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

e9a29bbe

Diff

@@ -95,7 +95,7 @@ noncomputable def Ideal.quotientEquivPiZmod (I : Ideal S) (b : Basis ι ℤ S) (
   let a := I.smithCoeffs b hI
   let e := I.quotientEquivPiSpan b hI
   let e' : (∀ i : ι, ℤ ⧸ Ideal.span ({a i} : Set ℤ)) ≃+ ∀ i : ι, ZMod (a i).natAbs :=
-    AddEquiv.piCongrRight fun i => ↑(Int.quotientSpanEquivZmod (a i))
+    AddEquiv.piCongrRight fun i => ↑(Int.quotientSpanEquivZMod (a i))
   (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : S ⧸ I ≃+ _).trans e'
 #align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZmod

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: small splits of RingTheory.Ideal.Operations; clean imports (#12090)

This is based on seeing the import RingTheory.Ideal.Operations → LinearAlgebra.Basis on the longest pole. It feels like Ideal.Operations is a bit of a chokepoint for compiling Mathlib since it imports many files and is imported by many files. So splitting out a few obvious parts should help with compile times. Moreover, there are a bunch of imports that I could remove and have the file still compile: presumably these are (were) transitive dependencies that shake does not remove.

The following results and their corollaries were split off:

Ideal.basisSpanSingleton
Basis.mem_ideal_iff
Ideal.colon

In particular, now Ideal.Operations should no longer need to know about Basis or submodule quotients.

46c2efe1

Diff

@@ -7,6 +7,7 @@ import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 import Mathlib.LinearAlgebra.FreeModule.PID
 import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathlib.LinearAlgebra.QuotientPi
+import Mathlib.RingTheory.Ideal.Basis
 
 #align_import linear_algebra.free_module.ideal_quotient from "leanprover-community/mathlib"@"90b0d53ee6ffa910e5c2a977ce7e2fc704647974"

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -24,7 +24,6 @@ namespace Ideal
 open scoped BigOperators DirectSum
 
 variable {ι R S : Type*} [CommRing R] [CommRing S] [Algebra R S]
-
 variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Finite ι]
 
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -115,7 +115,7 @@ variable (F : Type*) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F R
 noncomputable def quotientEquivDirectSum :
     (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ span ({I.smithCoeffs b hI i} : Set R) := by
   haveI := Fintype.ofFinite ι
-  -- porting note: manual construction of `CompatibleSMul` typeclass no longer needed
+  -- Porting note: manual construction of `CompatibleSMul` typeclass no longer needed
   exact ((I.quotientEquivPiSpan b _).restrictScalars F).trans
     (DirectSum.linearEquivFunOnFintype _ _ _).symm
 #align ideal.quotient_equiv_direct_sum Ideal.quotientEquivDirectSum

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -58,7 +58,7 @@ noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I 
   let I' : Submodule R (ι → R) := Submodule.pi Set.univ fun i => span ({a i} : Set R)
   have : Submodule.map (b'.equivFun : S →ₗ[R] ι → R) (I.restrictScalars R) = I' := by
     ext x
-    simp only [Submodule.mem_map, Submodule.mem_pi, mem_span_singleton, Set.mem_univ,
+    simp only [I', Submodule.mem_map, Submodule.mem_pi, mem_span_singleton, Set.mem_univ,
       Submodule.restrictScalars_mem, mem_I_iff, smul_eq_mul, forall_true_left, LinearEquiv.coe_coe,
       Basis.equivFun_apply]
     constructor

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
+import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 import Mathlib.LinearAlgebra.FreeModule.PID
 import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathlib.LinearAlgebra.QuotientPi

chore(*): use α → β instead of ∀ _ : α, β (#9529)

5618e431

Diff

@@ -76,7 +76,7 @@ noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I 
   · infer_instance
   classical
     let this :=
-      Submodule.quotientPi (show ∀ _, Submodule R R from fun i => span ({a i} : Set R))
+      Submodule.quotientPi (show _ → Submodule R R from fun i => span ({a i} : Set R))
     exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan

chore: Reorganize results about rank and finrank. (#9349)

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

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

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

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

0b41ea95

Diff

@@ -3,8 +3,6 @@ Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 -/
-import Mathlib.Data.ZMod.Quotient
-import Mathlib.LinearAlgebra.FreeModule.Finite.Rank
 import Mathlib.LinearAlgebra.FreeModule.PID
 import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathlib.LinearAlgebra.QuotientPi

chore: Nsmul -> NSMul, Zpow -> ZPow, etc (#9067)

Normalising to naming convention rule number 6.

9b2f0dca

Diff

@@ -116,7 +116,7 @@ variable (F : Type*) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F R
 noncomputable def quotientEquivDirectSum :
     (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ span ({I.smithCoeffs b hI i} : Set R) := by
   haveI := Fintype.ofFinite ι
-  -- porting note: manual construction of `CompatibleSmul` typeclass no longer needed
+  -- porting note: manual construction of `CompatibleSMul` typeclass no longer needed
   exact ((I.quotientEquivPiSpan b _).restrictScalars F).trans
     (DirectSum.linearEquivFunOnFintype _ _ _).symm
 #align ideal.quotient_equiv_direct_sum Ideal.quotientEquivDirectSum

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -24,7 +24,7 @@ namespace Ideal
 
 open scoped BigOperators DirectSum
 
-variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
+variable {ι R S : Type*} [CommRing R] [CommRing S] [Algebra R S]
 
 variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Finite ι]
 
@@ -108,7 +108,7 @@ noncomputable def fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finit
   classical exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
 
-variable (F : Type _) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F R S]
+variable (F : Type*) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F R S]
   (b : Basis ι R S) {I : Ideal S} (hI : I ≠ ⊥)
 
 /-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module linear_algebra.free_module.ideal_quotient
-! leanprover-community/mathlib commit 90b0d53ee6ffa910e5c2a977ce7e2fc704647974
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.ZMod.Quotient
 import Mathlib.LinearAlgebra.FreeModule.Finite.Rank
@@ -14,6 +9,8 @@ import Mathlib.LinearAlgebra.FreeModule.PID
 import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathlib.LinearAlgebra.QuotientPi
 
+#align_import linear_algebra.free_module.ideal_quotient from "leanprover-community/mathlib"@"90b0d53ee6ffa910e5c2a977ce7e2fc704647974"
+
 /-! # Ideals in free modules over PIDs
 
 ## Main results

chore: forward-port leanprover-community/mathlib#19121 (#4959)

4729d1cb

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.ideal_quotient
-! leanprover-community/mathlib commit d87199d51218d36a0a42c66c82d147b5a7ff87b3
+! leanprover-community/mathlib commit 90b0d53ee6ffa910e5c2a977ce7e2fc704647974
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -23,17 +23,19 @@ import Mathlib.LinearAlgebra.QuotientPi
 
 -/
 
+namespace Ideal
 
 open scoped BigOperators DirectSum
 
 variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
 
-variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Fintype ι]
+variable [IsDomain R] [IsPrincipalIdealRing R] [IsDomain S] [Finite ι]
 
 /-- We can write the quotient of an ideal over a PID as a product of quotients by principal ideals.
 -/
-noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I ≠ ⊥) :
-    (S ⧸ I) ≃ₗ[R] ∀ i, R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R) := by
+noncomputable def quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI : I ≠ ⊥) :
+    (S ⧸ I) ≃ₗ[R] ∀ i, R ⧸ span ({I.smithCoeffs b hI i} : Set R) := by
+  haveI := Fintype.ofFinite ι
   -- Choose `e : S ≃ₗ I` and a basis `b'` for `S` that turns the map
   -- `f := ((Submodule.subtype I).restrictScalars R).comp e` into a diagonal matrix:
   -- there is an `a : ι → ℤ` such that `f (b' i) = a i • b' i`.
@@ -57,10 +59,10 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
       exact ⟨c, b'.ext_elem fun i => Eq.trans (hc i) (this c i).symm⟩
   -- Now we map everything through the linear equiv `S ≃ₗ (ι → R)`,
   -- which maps `I` to `I' := Π i, a i ℤ`.
-  let I' : Submodule R (ι → R) := Submodule.pi Set.univ fun i => Ideal.span ({a i} : Set R)
+  let I' : Submodule R (ι → R) := Submodule.pi Set.univ fun i => span ({a i} : Set R)
   have : Submodule.map (b'.equivFun : S →ₗ[R] ι → R) (I.restrictScalars R) = I' := by
     ext x
-    simp only [Submodule.mem_map, Submodule.mem_pi, Ideal.mem_span_singleton, Set.mem_univ,
+    simp only [Submodule.mem_map, Submodule.mem_pi, mem_span_singleton, Set.mem_univ,
       Submodule.restrictScalars_mem, mem_I_iff, smul_eq_mul, forall_true_left, LinearEquiv.coe_coe,
       Basis.equivFun_apply]
     constructor
@@ -79,17 +81,17 @@ noncomputable def Ideal.quotientEquivPiSpan (I : Ideal S) (b : Basis ι R S) (hI
   · infer_instance
   classical
     let this :=
-      Submodule.quotientPi (show ∀ _, Submodule R R from fun i => Ideal.span ({a i} : Set R))
+      Submodule.quotientPi (show ∀ _, Submodule R R from fun i => span ({a i} : Set R))
     exact this
 #align ideal.quotient_equiv_pi_span Ideal.quotientEquivPiSpan
 
 /-- Ideal quotients over a free finite extension of `ℤ` are isomorphic to a direct product of
 `ZMod`. -/
-noncomputable def Ideal.quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
+noncomputable def quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (hI : I ≠ ⊥) :
     S ⧸ I ≃+ ∀ i, ZMod (I.smithCoeffs b hI i).natAbs :=
   let a := I.smithCoeffs b hI
   let e := I.quotientEquivPiSpan b hI
-  let e' : (∀ i : ι, ℤ ⧸ Ideal.span ({a i} : Set ℤ)) ≃+ ∀ i : ι, ZMod (a i).natAbs :=
+  let e' : (∀ i : ι, ℤ ⧸ span ({a i} : Set ℤ)) ≃+ ∀ i : ι, ZMod (a i).natAbs :=
     AddEquiv.piCongrRight fun i => ↑(Int.quotientSpanEquivZMod (a i))
   (↑(e : (S ⧸ I) ≃ₗ[ℤ] _) : S ⧸ I ≃+ _).trans e'
 #align ideal.quotient_equiv_pi_zmod Ideal.quotientEquivPiZMod
@@ -99,13 +101,13 @@ noncomputable def Ideal.quotientEquivPiZMod (I : Ideal S) (b : Basis ι ℤ S) (
 Can't be an instance because of the side condition `I ≠ ⊥`, and more importantly,
 because the choice of `Fintype` instance is non-canonical.
 -/
-noncomputable def Ideal.fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finite ℤ S]
+noncomputable def fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module.Finite ℤ S]
     (I : Ideal S) (hI : I ≠ ⊥) : Fintype (S ⧸ I) := by
   let b := Module.Free.chooseBasis ℤ S
   let a := I.smithCoeffs b hI
   let e := I.quotientEquivPiZMod b hI
   haveI : ∀ i, NeZero (a i).natAbs := fun i =>
-    ⟨Int.natAbs_ne_zero.mpr (Ideal.smithCoeffs_ne_zero b I hI i)⟩
+    ⟨Int.natAbs_ne_zero.mpr (smithCoeffs_ne_zero b I hI i)⟩
   classical exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
 
@@ -114,19 +116,21 @@ variable (F : Type _) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F
 
 /-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules
   (quotients by the ideals generated by Smith coefficients of `I`). -/
-noncomputable def Ideal.quotientEquivDirectSum :
-    (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R) :=
+noncomputable def quotientEquivDirectSum :
+    (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ span ({I.smithCoeffs b hI i} : Set R) := by
+  haveI := Fintype.ofFinite ι
   -- porting note: manual construction of `CompatibleSmul` typeclass no longer needed
-  ((I.quotientEquivPiSpan b _).restrictScalars F).trans
+  exact ((I.quotientEquivPiSpan b _).restrictScalars F).trans
     (DirectSum.linearEquivFunOnFintype _ _ _).symm
 #align ideal.quotient_equiv_direct_sum Ideal.quotientEquivDirectSum
 
-theorem Ideal.finrank_quotient_eq_sum [Nontrivial F]
-    [∀ i, Module.Free F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))]
-    [∀ i, Module.Finite F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))] :
+theorem finrank_quotient_eq_sum {ι} [Fintype ι] (b : Basis ι R S) [Nontrivial F]
+    [∀ i, Module.Free F (R ⧸ span ({I.smithCoeffs b hI i} : Set R))]
+    [∀ i, Module.Finite F (R ⧸ span ({I.smithCoeffs b hI i} : Set R))] :
     FiniteDimensional.finrank F (S ⧸ I) =
-      ∑ i, FiniteDimensional.finrank F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R)) := by
+      ∑ i, FiniteDimensional.finrank F (R ⧸ span ({I.smithCoeffs b hI i} : Set R)) := by
   -- slow, and dot notation doesn't work
-  rw [LinearEquiv.finrank_eq <| Ideal.quotientEquivDirectSum F b hI,
-    FiniteDimensional.finrank_directSum]
+  rw [LinearEquiv.finrank_eq <| quotientEquivDirectSum F b hI, FiniteDimensional.finrank_directSum]
 #align ideal.finrank_quotient_eq_sum Ideal.finrank_quotient_eq_sum
+
+end Ideal

linear_algebra.free_module.ideal_quotient@6623e6af705e97002a9054c1c05a980180276fc1..d87199d51218d36a0a42c66c82d147b5a7ff87b3

chore: forward-port leanprover-community/mathlib#19084 (file 2 of 2) (#4821)

03c3ef63

Diff

@@ -4,13 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.ideal_quotient
-! leanprover-community/mathlib commit 6623e6af705e97002a9054c1c05a980180276fc1
+! leanprover-community/mathlib commit d87199d51218d36a0a42c66c82d147b5a7ff87b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.ZMod.Quotient
-import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
+import Mathlib.LinearAlgebra.FreeModule.Finite.Rank
 import Mathlib.LinearAlgebra.FreeModule.PID
+import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 import Mathlib.LinearAlgebra.QuotientPi
 
 /-! # Ideals in free modules over PIDs
@@ -23,7 +24,7 @@ import Mathlib.LinearAlgebra.QuotientPi
 -/
 
 
-open BigOperators
+open scoped BigOperators DirectSum
 
 variable {ι R S : Type _} [CommRing R] [CommRing S] [Algebra R S]
 
@@ -107,3 +108,25 @@ noncomputable def Ideal.fintypeQuotientOfFreeOfNeBot [Module.Free ℤ S] [Module
     ⟨Int.natAbs_ne_zero.mpr (Ideal.smithCoeffs_ne_zero b I hI i)⟩
   classical exact Fintype.ofEquiv (∀ i, ZMod (a i).natAbs) e.symm
 #align ideal.fintype_quotient_of_free_of_ne_bot Ideal.fintypeQuotientOfFreeOfNeBot
+
+variable (F : Type _) [CommRing F] [Algebra F R] [Algebra F S] [IsScalarTower F R S]
+  (b : Basis ι R S) {I : Ideal S} (hI : I ≠ ⊥)
+
+/-- Decompose `S⧸I` as a direct sum of cyclic `R`-modules
+  (quotients by the ideals generated by Smith coefficients of `I`). -/
+noncomputable def Ideal.quotientEquivDirectSum :
+    (S ⧸ I) ≃ₗ[F] ⨁ i, R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R) :=
+  -- porting note: manual construction of `CompatibleSmul` typeclass no longer needed
+  ((I.quotientEquivPiSpan b _).restrictScalars F).trans
+    (DirectSum.linearEquivFunOnFintype _ _ _).symm
+#align ideal.quotient_equiv_direct_sum Ideal.quotientEquivDirectSum
+
+theorem Ideal.finrank_quotient_eq_sum [Nontrivial F]
+    [∀ i, Module.Free F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))]
+    [∀ i, Module.Finite F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R))] :
+    FiniteDimensional.finrank F (S ⧸ I) =
+      ∑ i, FiniteDimensional.finrank F (R ⧸ Ideal.span ({I.smithCoeffs b hI i} : Set R)) := by
+  -- slow, and dot notation doesn't work
+  rw [LinearEquiv.finrank_eq <| Ideal.quotientEquivDirectSum F b hI,
+    FiniteDimensional.finrank_directSum]
+#align ideal.finrank_quotient_eq_sum Ideal.finrank_quotient_eq_sum