ring_theory.localization.module ⟷ Mathlib.RingTheory.Localization.Module

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

@@ -81,15 +81,15 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
   choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
   have h0 : algebraMap A Aₛ (∑ i in s, g' i • v i) = 0 :=
     by
-    apply_fun (· • ·) (a : R) at hg 
-    rw [smul_zero, Finset.smul_sum] at hg 
+    apply_fun (· • ·) (a : R) at hg
+    rw [smul_zero, Finset.smul_sum] at hg
     rw [map_sum, ← hg]
     refine' Finset.sum_congr rfl fun i hi => _
     rw [← smul_assoc, ← hg' i hi, Algebra.smul_def, map_mul, ← IsScalarTower.algebraMap_apply, ←
       Algebra.smul_def, algebraMap_smul]
   obtain ⟨⟨_, r, hrS, rfl⟩, hr : algebraMap R A r * _ = 0⟩ :=
     (IsLocalization.map_eq_zero_iff (Algebra.algebraMapSubmonoid A S) _ _).1 h0
-  simp_rw [Finset.mul_sum, ← Algebra.smul_def, smul_smul] at hr 
+  simp_rw [Finset.mul_sum, ← Algebra.smul_def, smul_smul] at hr
   specialize hv s _ hr i hi
   rw [← (IsLocalization.map_units Rₛ a).mul_right_eq_zero, ← Algebra.smul_def, ← hg' i hi]
   exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨⟨r, hrS⟩, hv⟩

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

@@ -96,8 +96,8 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
 #align linear_independent.localization_localization LinearIndependent.localization_localization
 -/
 
-#print SpanEqTop.localization_localization /-
-theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
+#print span_eq_top_localization_localization /-
+theorem span_eq_top_localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
   rw [eq_top_iff]
   rintro a' -
@@ -111,7 +111,7 @@ theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
   rw [← Algebra.coe_linearMap, ← LinearMap.coe_restrictScalars R, ← LinearMap.map_span]
   exact mem_map_of_mem (hv.symm ▸ mem_top)
   · infer_instance
-#align span_eq_top.localization_localization SpanEqTop.localization_localization
+#align span_eq_top.localization_localization span_eq_top_localization_localization
 -/
 
 #print Basis.localizationLocalization /-
@@ -122,7 +122,7 @@ A suitable instance for `[algebra A Aₛ]` is `localization_algebra`.
 noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A) : Basis ι Rₛ Aₛ :=
   Basis.mk (b.LinearIndependent.localization_localization _ S _)
     (by
-      rw [Set.range_comp, SpanEqTop.localization_localization Rₛ S Aₛ b.span_eq]
+      rw [Set.range_comp, span_eq_top_localization_localization Rₛ S Aₛ b.span_eq]
       exact le_rfl)
 #align basis.localization_localization Basis.localizationLocalization
 -/

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

@@ -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: Junyan Xu, Anne Baanen
 -/
-import Mathbin.LinearAlgebra.Basis
-import Mathbin.RingTheory.Localization.FractionRing
-import Mathbin.RingTheory.Localization.Integer
+import LinearAlgebra.Basis
+import RingTheory.Localization.FractionRing
+import RingTheory.Localization.Integer
 
 #align_import ring_theory.localization.module from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.module
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Basis
 import Mathbin.RingTheory.Localization.FractionRing
 import Mathbin.RingTheory.Localization.Integer
 
+#align_import ring_theory.localization.module from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Modules / vector spaces over localizations / fraction fields
 

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

@@ -41,12 +41,11 @@ variable {R : Type _} (Rₛ : Type _) [CommRing R] [CommRing Rₛ] [Algebra R R
 
 variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
 
-include hT
-
 section AddCommMonoid
 
 variable {M : Type _} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
 
+#print LinearIndependent.localization /-
 theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
   rw [linearIndependent_iff'] at hli ⊢
@@ -60,6 +59,7 @@ theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : Linea
   refine' (IsLocalization.map_units Rₛ a).mul_right_eq_zero.mp _
   rw [← Algebra.smul_def, ← map_zero (algebraMap R Rₛ), ← hli, hg' i hi]
 #align linear_independent.localization LinearIndependent.localization
+-/
 
 end AddCommMonoid
 
@@ -73,10 +73,9 @@ variable [Algebra Rₛ Aₛ] [Algebra R Aₛ] [IsScalarTower R Rₛ Aₛ] [IsSca
 
 variable [hA : IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ]
 
-include hA
-
 open Submodule
 
+#print LinearIndependent.localization_localization /-
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) :=
   by
@@ -98,7 +97,9 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
   rw [← (IsLocalization.map_units Rₛ a).mul_right_eq_zero, ← Algebra.smul_def, ← hg' i hi]
   exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨⟨r, hrS⟩, hv⟩
 #align linear_independent.localization_localization LinearIndependent.localization_localization
+-/
 
+#print SpanEqTop.localization_localization /-
 theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
   rw [eq_top_iff]
@@ -114,6 +115,7 @@ theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
   exact mem_map_of_mem (hv.symm ▸ mem_top)
   · infer_instance
 #align span_eq_top.localization_localization SpanEqTop.localization_localization
+-/
 
 #print Basis.localizationLocalization /-
 /-- If `A` has an `R`-basis, then localizing `A` at `S` has a basis over `R` localized at `S`.
@@ -128,12 +130,15 @@ noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A
 #align basis.localization_localization Basis.localizationLocalization
 -/
 
+#print Basis.localizationLocalization_apply /-
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
     b.localization_localization Rₛ S Aₛ i = algebraMap A Aₛ (b i) :=
   Basis.mk_apply _ _ _
 #align basis.localization_localization_apply Basis.localizationLocalization_apply
+-/
 
+#print Basis.localizationLocalization_repr_algebraMap /-
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :
     (b.localization_localization Rₛ S Aₛ).repr (algebraMap A Aₛ x) i =
@@ -154,6 +159,7 @@ theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis
         simp [finsupp.not_mem_support_iff.mp hi])
     _ = algebraMap R Rₛ (b.repr x i) := by simp [Algebra.smul_def]
 #align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMap
+-/
 
 end LocalizationLocalization
 
@@ -165,11 +171,13 @@ variable (R K : Type _) [CommRing R] [Field K] [Algebra R K] [IsFractionRing R K
 
 variable {V : Type _} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
 
+#print LinearIndependent.iff_fractionRing /-
 theorem LinearIndependent.iff_fractionRing {ι : Type _} {b : ι → V} :
     LinearIndependent R b ↔ LinearIndependent K b :=
   ⟨LinearIndependent.localization K R⁰,
     LinearIndependent.restrict_scalars (smul_left_injective R one_ne_zero)⟩
 #align linear_independent.iff_fraction_ring LinearIndependent.iff_fractionRing
+-/
 
 end FractionRing
 

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

@@ -153,7 +153,6 @@ theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis
       (Finset.sum_eq_single i (fun j _ hj => by simp [hj]) fun hi => by
         simp [finsupp.not_mem_support_iff.mp hi])
     _ = algebraMap R Rₛ (b.repr x i) := by simp [Algebra.smul_def]
-    
 #align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMap
 
 end LocalizationLocalization

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

@@ -85,7 +85,7 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
   choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
   have h0 : algebraMap A Aₛ (∑ i in s, g' i • v i) = 0 :=
     by
-    apply_fun (· • ·) (a : R)  at hg 
+    apply_fun (· • ·) (a : R) at hg 
     rw [smul_zero, Finset.smul_sum] at hg 
     rw [map_sum, ← hg]
     refine' Finset.sum_congr rfl fun i hi => _

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

@@ -49,7 +49,7 @@ variable {M : Type _} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTo
 
 theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
-  rw [linearIndependent_iff'] at hli⊢
+  rw [linearIndependent_iff'] at hli ⊢
   intro s g hg i hi
   choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
   specialize hli s g' _ i hi
@@ -80,20 +80,20 @@ open Submodule
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) :=
   by
-  rw [linearIndependent_iff'] at hv⊢
+  rw [linearIndependent_iff'] at hv ⊢
   intro s g hg i hi
   choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
   have h0 : algebraMap A Aₛ (∑ i in s, g' i • v i) = 0 :=
     by
-    apply_fun (· • ·) (a : R)  at hg
-    rw [smul_zero, Finset.smul_sum] at hg
+    apply_fun (· • ·) (a : R)  at hg 
+    rw [smul_zero, Finset.smul_sum] at hg 
     rw [map_sum, ← hg]
     refine' Finset.sum_congr rfl fun i hi => _
     rw [← smul_assoc, ← hg' i hi, Algebra.smul_def, map_mul, ← IsScalarTower.algebraMap_apply, ←
       Algebra.smul_def, algebraMap_smul]
   obtain ⟨⟨_, r, hrS, rfl⟩, hr : algebraMap R A r * _ = 0⟩ :=
     (IsLocalization.map_eq_zero_iff (Algebra.algebraMapSubmonoid A S) _ _).1 h0
-  simp_rw [Finset.mul_sum, ← Algebra.smul_def, smul_smul] at hr
+  simp_rw [Finset.mul_sum, ← Algebra.smul_def, smul_smul] at hr 
   specialize hv s _ hr i hi
   rw [← (IsLocalization.map_units Rₛ a).mul_right_eq_zero, ← Algebra.smul_def, ← hg' i hi]
   exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨⟨r, hrS⟩, hv⟩

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

@@ -31,9 +31,9 @@ This file contains some results about vector spaces over the field of fractions
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
-open nonZeroDivisors
+open scoped nonZeroDivisors
 
 section Localization
 

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

@@ -47,12 +47,6 @@ section AddCommMonoid
 
 variable {M : Type _} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
 
-/- warning: linear_independent.localization -> LinearIndependent.localization is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {M : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] [_inst_6 : Module.{u2, u3} Rₛ M (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R Rₛ M (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} Rₛ M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} Rₛ M (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} Rₛ M (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} Rₛ M (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_5))))] {ι : Type.{u4}} {b : ι -> M}, (LinearIndependent.{u4, u1, u3} ι R M b (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_5) -> (LinearIndependent.{u4, u2, u3} ι Rₛ M b (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4 _inst_6)
-but is expected to have type
-  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] [_inst_6 : Module.{u1, u2} Rₛ M (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_4] [_inst_7 : IsScalarTower.{u3, u1, u2} R Rₛ M (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (SMulZeroClass.toSMul.{u1, u2} Rₛ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u2} Rₛ M (CommMonoidWithZero.toZero.{u1} Rₛ (CommSemiring.toCommMonoidWithZero.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u2} Rₛ M (Semiring.toMonoidWithZero.{u1} Rₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u1, u2} Rₛ M (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_5))))] {ι : Type.{u4}} {b : ι -> M}, (LinearIndependent.{u4, u3, u2} ι R M b (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_5) -> (LinearIndependent.{u4, u1, u2} ι Rₛ M b (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_4 _inst_6)
-Case conversion may be inaccurate. Consider using '#align linear_independent.localization LinearIndependent.localizationₓ'. -/
 theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
   rw [linearIndependent_iff'] at hli⊢
@@ -83,9 +77,6 @@ include hA
 
 open Submodule
 
-/- warning: linear_independent.localization_localization -> LinearIndependent.localization_localization is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_independent.localization_localization LinearIndependent.localization_localizationₓ'. -/
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) :=
   by
@@ -108,9 +99,6 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
   exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨⟨r, hrS⟩, hv⟩
 #align linear_independent.localization_localization LinearIndependent.localization_localization
 
-/- warning: span_eq_top.localization_localization -> SpanEqTop.localization_localization is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align span_eq_top.localization_localization SpanEqTop.localization_localizationₓ'. -/
 theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
   rw [eq_top_iff]
@@ -140,18 +128,12 @@ noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A
 #align basis.localization_localization Basis.localizationLocalization
 -/
 
-/- warning: basis.localization_localization_apply -> Basis.localizationLocalization_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.localization_localization_apply Basis.localizationLocalization_applyₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
     b.localization_localization Rₛ S Aₛ i = algebraMap A Aₛ (b i) :=
   Basis.mk_apply _ _ _
 #align basis.localization_localization_apply Basis.localizationLocalization_apply
 
-/- warning: basis.localization_localization_repr_algebra_map -> Basis.localizationLocalization_repr_algebraMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMapₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :
     (b.localization_localization Rₛ S Aₛ).repr (algebraMap A Aₛ x) i =
@@ -184,12 +166,6 @@ variable (R K : Type _) [CommRing R] [Field K] [Algebra R K] [IsFractionRing R K
 
 variable {V : Type _} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
 
-/- warning: linear_independent.iff_fraction_ring -> LinearIndependent.iff_fractionRing is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (K : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : Field.{u2} K] [_inst_3 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_4 : IsFractionRing.{u1, u2} R _inst_1 K (Field.toCommRing.{u2} K _inst_2) _inst_3] {V : Type.{u3}} [_inst_5 : AddCommGroup.{u3} V] [_inst_6 : Module.{u1, u3} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)] [_inst_7 : Module.{u2, u3} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u2, u3} R K V (SMulZeroClass.toHasSmul.{u1, u2} R K (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R K (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R K (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} R K (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Algebra.toModule.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} K V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u3} K V (MulZeroClass.toHasZero.{u2} K (MulZeroOneClass.toMulZeroClass.{u2} K (MonoidWithZero.toMulZeroOneClass.{u2} K (Semiring.toMonoidWithZero.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u3} K V (Semiring.toMonoidWithZero.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (Module.toMulActionWithZero.{u2, u3} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u3} R V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R V (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R V (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (Module.toMulActionWithZero.{u1, u3} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_6))))] {ι : Type.{u4}} {b : ι -> V}, Iff (LinearIndependent.{u4, u1, u3} ι R V b (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_6) (LinearIndependent.{u4, u2, u3} ι K V b (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_7)
-but is expected to have type
-  forall (R : Type.{u3}) (K : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : Field.{u1} K] [_inst_3 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_4 : IsFractionRing.{u3, u1} R _inst_1 K (Field.toCommRing.{u1} K _inst_2) _inst_3] {V : Type.{u2}} [_inst_5 : AddCommGroup.{u2} V] [_inst_6 : Module.{u3, u2} R V (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_7 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_8 : IsScalarTower.{u3, u1, u2} R K V (Algebra.toSMul.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_3) (SMulZeroClass.toSMul.{u1, u2} K V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u2} K V (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K V (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u3, u2} R V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R V (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R V (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u3, u2} R V (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6))))] {ι : Type.{u4}} {b : ι -> V}, Iff (LinearIndependent.{u4, u3, u2} ι R V b (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6) (LinearIndependent.{u4, u1, u2} ι K V b (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)
-Case conversion may be inaccurate. Consider using '#align linear_independent.iff_fraction_ring LinearIndependent.iff_fractionRingₓ'. -/
 theorem LinearIndependent.iff_fractionRing {ι : Type _} {b : ι → V} :
     LinearIndependent R b ↔ LinearIndependent K b :=
   ⟨LinearIndependent.localization K R⁰,

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

@@ -84,10 +84,7 @@ include hA
 open Submodule
 
 /- warning: linear_independent.localization_localization -> LinearIndependent.localization_localization is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u1, u3} ι R A v (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u4} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u4} ι A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))
-but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u4, u3} ι R A v (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u1} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u1} ι A Aₛ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7)) v) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_independent.localization_localization LinearIndependent.localization_localizationₓ'. -/
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) :=
@@ -112,10 +109,7 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
 #align linear_independent.localization_localization LinearIndependent.localization_localization
 
 /- warning: span_eq_top.localization_localization -> SpanEqTop.localization_localization is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {v : Set.{u3} A}, (Eq.{succ u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.span.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) v) (Top.top.{u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.hasTop.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)))) -> (Eq.{succ u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Set.image.{u3, u4} A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.hasTop.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))
-but is expected to have type
-  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u4}} [_inst_4 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u3, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u3, u4, u2} R A Aₛ (Algebra.toSMul.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) (Algebra.toSMul.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u4, u2} A (CommRing.toCommSemiring.{u4} A _inst_4) (Algebra.algebraMapSubmonoid.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {v : Set.{u4} A}, (Eq.{succ u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.span.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) v) (Top.top.{u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.instTopSubmodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)))) -> (Eq.{succ u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Set.image.{u4, u2} A Aₛ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.instTopSubmodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align span_eq_top.localization_localization SpanEqTop.localization_localizationₓ'. -/
 theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
@@ -147,10 +141,7 @@ noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A
 -/
 
 /- warning: basis.localization_localization_apply -> Basis.localizationLocalization_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u4} Aₛ (coeFn.{max (succ u5) (succ u2) (succ u4), max (succ u5) (succ u4)} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (fun (_x : Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) => ι -> Aₛ) (FunLike.hasCoeToFun.{max (succ u5) (succ u2) (succ u4), succ u5, succ u4} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => Aₛ) (Basis.funLike.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) (coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (fun (_x : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) => ι -> A) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => A) (Basis.funLike.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))) b i))
-but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u2} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u2} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u5), succ u5, succ u2} (Basis.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) _x) (Basis.funLike.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Basis.localizationLocalization.{u4, u1, u3, u2, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => A) _x) (Basis.funLike.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) b i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.localization_localization_apply Basis.localizationLocalization_applyₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
@@ -159,10 +150,7 @@ theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i
 #align basis.localization_localization_apply Basis.localizationLocalization_apply
 
 /- warning: basis.localization_localization_repr_algebra_map -> Basis.localizationLocalization_repr_algebraMap is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} Rₛ (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (fun (_x : Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) => ι -> Rₛ) (Finsupp.coeFun.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (coeFn.{max (succ u4) (succ (max u5 u2)), max (succ u4) (succ (max u5 u2))} (LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (fun (_x : LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) => Aₛ -> (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (LinearEquiv.hasCoeToFun.{u2, u2, u4, max u5 u2} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (Basis.repr.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) x)) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (fun (_x : RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) => R -> Rₛ) (RingHom.hasCoeToFun.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (algebraMap.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (coeFn.{max (succ u5) (succ u1), max (succ u5) (succ u1)} (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u3) (succ (max u5 u1)), max (succ u3) (succ (max u5 u1))} (LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => A -> (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u5 u1} R R A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) b) x) i))
-but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) b) x) i))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMapₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :

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

@@ -162,7 +162,7 @@ theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} Rₛ (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (fun (_x : Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) => ι -> Rₛ) (Finsupp.coeFun.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (coeFn.{max (succ u4) (succ (max u5 u2)), max (succ u4) (succ (max u5 u2))} (LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (fun (_x : LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) => Aₛ -> (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (LinearEquiv.hasCoeToFun.{u2, u2, u4, max u5 u2} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (Basis.repr.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) x)) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (fun (_x : RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) => R -> Rₛ) (RingHom.hasCoeToFun.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (algebraMap.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (coeFn.{max (succ u5) (succ u1), max (succ u5) (succ u1)} (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u3) (succ (max u5 u1)), max (succ u3) (succ (max u5 u1))} (LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => A -> (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u5 u1} R R A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) b) x) i))
 but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) b) x) i))
+  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) b) x) i))
 Case conversion may be inaccurate. Consider using '#align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMapₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :

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

@@ -87,7 +87,7 @@ open Submodule
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u1, u3} ι R A v (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u4} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u4} ι A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))
 but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u4, u3} ι R A v (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u1} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u1} ι A Aₛ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7)) v) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))
+  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u4, u3} ι R A v (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u1} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u1} ι A Aₛ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7)) v) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))
 Case conversion may be inaccurate. Consider using '#align linear_independent.localization_localization LinearIndependent.localization_localizationₓ'. -/
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) :=
@@ -115,7 +115,7 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {v : Set.{u3} A}, (Eq.{succ u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.span.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) v) (Top.top.{u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.hasTop.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)))) -> (Eq.{succ u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Set.image.{u3, u4} A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.hasTop.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))
 but is expected to have type
-  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u4}} [_inst_4 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u3, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u3, u4, u2} R A Aₛ (Algebra.toSMul.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) (Algebra.toSMul.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u4, u2} A (CommRing.toCommSemiring.{u4} A _inst_4) (Algebra.algebraMapSubmonoid.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {v : Set.{u4} A}, (Eq.{succ u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.span.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) v) (Top.top.{u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.instTopSubmodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)))) -> (Eq.{succ u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Set.image.{u4, u2} A Aₛ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.instTopSubmodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8))))
+  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u4}} [_inst_4 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u3, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u3, u4, u2} R A Aₛ (Algebra.toSMul.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) (Algebra.toSMul.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u4, u2} A (CommRing.toCommSemiring.{u4} A _inst_4) (Algebra.algebraMapSubmonoid.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {v : Set.{u4} A}, (Eq.{succ u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.span.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) v) (Top.top.{u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.instTopSubmodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)))) -> (Eq.{succ u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Set.image.{u4, u2} A Aₛ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.instTopSubmodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8))))
 Case conversion may be inaccurate. Consider using '#align span_eq_top.localization_localization SpanEqTop.localization_localizationₓ'. -/
 theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
@@ -150,7 +150,7 @@ noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u4} Aₛ (coeFn.{max (succ u5) (succ u2) (succ u4), max (succ u5) (succ u4)} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (fun (_x : Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) => ι -> Aₛ) (FunLike.hasCoeToFun.{max (succ u5) (succ u2) (succ u4), succ u5, succ u4} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => Aₛ) (Basis.funLike.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) (coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (fun (_x : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) => ι -> A) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => A) (Basis.funLike.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))) b i))
 but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u2} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u2} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u5), succ u5, succ u2} (Basis.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) _x) (Basis.funLike.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Basis.localizationLocalization.{u4, u1, u3, u2, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => A) _x) (Basis.funLike.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) b i))
+  forall {R : Type.{u4}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u2} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u2} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u5), succ u5, succ u2} (Basis.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) _x) (Basis.funLike.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Basis.localizationLocalization.{u4, u1, u3, u2, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => A) _x) (Basis.funLike.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) b i))
 Case conversion may be inaccurate. Consider using '#align basis.localization_localization_apply Basis.localizationLocalization_applyₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
@@ -162,7 +162,7 @@ theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} Rₛ (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (fun (_x : Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) => ι -> Rₛ) (Finsupp.coeFun.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (coeFn.{max (succ u4) (succ (max u5 u2)), max (succ u4) (succ (max u5 u2))} (LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (fun (_x : LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) => Aₛ -> (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (LinearEquiv.hasCoeToFun.{u2, u2, u4, max u5 u2} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (Basis.repr.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) x)) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (fun (_x : RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) => R -> Rₛ) (RingHom.hasCoeToFun.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (algebraMap.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (coeFn.{max (succ u5) (succ u1), max (succ u5) (succ u1)} (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u3) (succ (max u5 u1)), max (succ u3) (succ (max u5 u1))} (LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => A -> (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u5 u1} R R A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) b) x) i))
 but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) b) x) i))
+  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) b) x) i))
 Case conversion may be inaccurate. Consider using '#align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMapₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :

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

@@ -51,7 +51,7 @@ variable {M : Type _} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTo
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {M : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] [_inst_6 : Module.{u2, u3} Rₛ M (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R Rₛ M (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} Rₛ M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} Rₛ M (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} Rₛ M (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} Rₛ M (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_5))))] {ι : Type.{u4}} {b : ι -> M}, (LinearIndependent.{u4, u1, u3} ι R M b (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_5) -> (LinearIndependent.{u4, u2, u3} ι Rₛ M b (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4 _inst_6)
 but is expected to have type
-  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) _inst_4] [_inst_6 : Module.{u1, u2} Rₛ M (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_4] [_inst_7 : IsScalarTower.{u3, u1, u2} R Rₛ M (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_3) (SMulZeroClass.toSMul.{u1, u2} Rₛ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u2} Rₛ M (CommMonoidWithZero.toZero.{u1} Rₛ (CommSemiring.toCommMonoidWithZero.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u2} Rₛ M (Semiring.toMonoidWithZero.{u1} Rₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u1, u2} Rₛ M (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) _inst_4 _inst_5))))] {ι : Type.{u4}} {b : ι -> M}, (LinearIndependent.{u4, u3, u2} ι R M b (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) _inst_4 _inst_5) -> (LinearIndependent.{u4, u1, u2} ι Rₛ M b (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_4 _inst_6)
+  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4] [_inst_6 : Module.{u1, u2} Rₛ M (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_4] [_inst_7 : IsScalarTower.{u3, u1, u2} R Rₛ M (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (SMulZeroClass.toSMul.{u1, u2} Rₛ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u2} Rₛ M (CommMonoidWithZero.toZero.{u1} Rₛ (CommSemiring.toCommMonoidWithZero.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u2} Rₛ M (Semiring.toMonoidWithZero.{u1} Rₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u1, u2} Rₛ M (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_5))))] {ι : Type.{u4}} {b : ι -> M}, (LinearIndependent.{u4, u3, u2} ι R M b (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) _inst_4 _inst_5) -> (LinearIndependent.{u4, u1, u2} ι Rₛ M b (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_4 _inst_6)
 Case conversion may be inaccurate. Consider using '#align linear_independent.localization LinearIndependent.localizationₓ'. -/
 theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
@@ -87,7 +87,7 @@ open Submodule
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u1, u3} ι R A v (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u4} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u4} ι A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))
 but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u4, u3} ι R A v (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u1} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u1} ι A Aₛ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7)) v) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8))
+  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u4, u3} ι R A v (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u1} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u1} ι A Aₛ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7)) v) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))
 Case conversion may be inaccurate. Consider using '#align linear_independent.localization_localization LinearIndependent.localization_localizationₓ'. -/
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) :=
@@ -115,7 +115,7 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {v : Set.{u3} A}, (Eq.{succ u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.span.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) v) (Top.top.{u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.hasTop.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)))) -> (Eq.{succ u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Set.image.{u3, u4} A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.hasTop.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))
 but is expected to have type
-  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u4}} [_inst_4 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u3, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u3, u4, u2} R A Aₛ (Algebra.toSMul.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5) (Algebra.toSMul.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u4, u2} A (CommRing.toCommSemiring.{u4} A _inst_4) (Algebra.algebraMapSubmonoid.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) A (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {v : Set.{u4} A}, (Eq.{succ u4} (Submodule.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5)) (Submodule.span.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5) v) (Top.top.{u4} (Submodule.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5)) (Submodule.instTopSubmodule.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5)))) -> (Eq.{succ u2} (Submodule.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8) (Set.image.{u4, u2} A Aₛ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))))) (algebraMap.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u2} (Submodule.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.instTopSubmodule.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8))))
+  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u4}} [_inst_4 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u3, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u3, u4, u2} R A Aₛ (Algebra.toSMul.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) (Algebra.toSMul.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u4, u2} A (CommRing.toCommSemiring.{u4} A _inst_4) (Algebra.algebraMapSubmonoid.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {v : Set.{u4} A}, (Eq.{succ u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.span.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5) v) (Top.top.{u4} (Submodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)) (Submodule.instTopSubmodule.{u3, u4} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)) _inst_5)))) -> (Eq.{succ u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Set.image.{u4, u2} A Aₛ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u2} (Submodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.instTopSubmodule.{u1, u2} Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8))))
 Case conversion may be inaccurate. Consider using '#align span_eq_top.localization_localization SpanEqTop.localization_localizationₓ'. -/
 theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
@@ -150,7 +150,7 @@ noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u4} Aₛ (coeFn.{max (succ u5) (succ u2) (succ u4), max (succ u5) (succ u4)} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (fun (_x : Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) => ι -> Aₛ) (FunLike.hasCoeToFun.{max (succ u5) (succ u2) (succ u4), succ u5, succ u4} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => Aₛ) (Basis.funLike.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) (coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (fun (_x : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) => ι -> A) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => A) (Basis.funLike.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))) b i))
 but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u2} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u2} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u5), succ u5, succ u2} (Basis.{u5, u1, u2} ι Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) _x) (Basis.funLike.{u5, u1, u2} ι Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) (Basis.localizationLocalization.{u4, u1, u3, u2, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))))) (algebraMap.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => A) _x) (Basis.funLike.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) b i))
+  forall {R : Type.{u4}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u2} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u2} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u5), succ u5, succ u2} (Basis.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) _x) (Basis.funLike.{u5, u1, u2} ι Rₛ Aₛ (CommSemiring.toSemiring.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_8)) (Basis.localizationLocalization.{u4, u1, u3, u2, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6))))))) (algebraMap.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u2} Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6)) _inst_7) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => A) _x) (Basis.funLike.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) b i))
 Case conversion may be inaccurate. Consider using '#align basis.localization_localization_apply Basis.localizationLocalization_applyₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
@@ -162,7 +162,7 @@ theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i
 lean 3 declaration is
   forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} Rₛ (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (fun (_x : Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) => ι -> Rₛ) (Finsupp.coeFun.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (coeFn.{max (succ u4) (succ (max u5 u2)), max (succ u4) (succ (max u5 u2))} (LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (fun (_x : LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) => Aₛ -> (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (LinearEquiv.hasCoeToFun.{u2, u2, u4, max u5 u2} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (Basis.repr.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) x)) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (fun (_x : RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) => R -> Rₛ) (RingHom.hasCoeToFun.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (algebraMap.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (coeFn.{max (succ u5) (succ u1), max (succ u5) (succ u1)} (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u3) (succ (max u5 u1)), max (succ u3) (succ (max u5 u1))} (LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => A -> (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u5 u1} R R A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) b) x) i))
 but is expected to have type
-  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) b) x) i))
+  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (CommSemiring.toSemiring.{u1} Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5) b) x) i))
 Case conversion may be inaccurate. Consider using '#align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMapₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :
@@ -200,7 +200,7 @@ variable {V : Type _} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower
 lean 3 declaration is
   forall (R : Type.{u1}) (K : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : Field.{u2} K] [_inst_3 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_4 : IsFractionRing.{u1, u2} R _inst_1 K (Field.toCommRing.{u2} K _inst_2) _inst_3] {V : Type.{u3}} [_inst_5 : AddCommGroup.{u3} V] [_inst_6 : Module.{u1, u3} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)] [_inst_7 : Module.{u2, u3} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u2, u3} R K V (SMulZeroClass.toHasSmul.{u1, u2} R K (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R K (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R K (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} R K (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Algebra.toModule.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} K V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u3} K V (MulZeroClass.toHasZero.{u2} K (MulZeroOneClass.toMulZeroClass.{u2} K (MonoidWithZero.toMulZeroOneClass.{u2} K (Semiring.toMonoidWithZero.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u3} K V (Semiring.toMonoidWithZero.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (Module.toMulActionWithZero.{u2, u3} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u3} R V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R V (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R V (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (Module.toMulActionWithZero.{u1, u3} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_6))))] {ι : Type.{u4}} {b : ι -> V}, Iff (LinearIndependent.{u4, u1, u3} ι R V b (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_6) (LinearIndependent.{u4, u2, u3} ι K V b (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_7)
 but is expected to have type
-  forall (R : Type.{u3}) (K : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : Field.{u1} K] [_inst_3 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_4 : IsFractionRing.{u3, u1} R _inst_1 K (Field.toCommRing.{u1} K _inst_2) _inst_3] {V : Type.{u2}} [_inst_5 : AddCommGroup.{u2} V] [_inst_6 : Module.{u3, u2} R V (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_7 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_8 : IsScalarTower.{u3, u1, u2} R K V (Algebra.toSMul.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_3) (SMulZeroClass.toSMul.{u1, u2} K V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u2} K V (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K V (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u3, u2} R V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R V (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R V (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u3, u2} R V (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6))))] {ι : Type.{u4}} {b : ι -> V}, Iff (LinearIndependent.{u4, u3, u2} ι R V b (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6) (LinearIndependent.{u4, u1, u2} ι K V b (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)
+  forall (R : Type.{u3}) (K : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : Field.{u1} K] [_inst_3 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_4 : IsFractionRing.{u3, u1} R _inst_1 K (Field.toCommRing.{u1} K _inst_2) _inst_3] {V : Type.{u2}} [_inst_5 : AddCommGroup.{u2} V] [_inst_6 : Module.{u3, u2} R V (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_7 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_8 : IsScalarTower.{u3, u1, u2} R K V (Algebra.toSMul.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_3) (SMulZeroClass.toSMul.{u1, u2} K V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u2} K V (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K V (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u3, u2} R V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R V (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R V (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u3, u2} R V (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6))))] {ι : Type.{u4}} {b : ι -> V}, Iff (LinearIndependent.{u4, u3, u2} ι R V b (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6) (LinearIndependent.{u4, u1, u2} ι K V b (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)
 Case conversion may be inaccurate. Consider using '#align linear_independent.iff_fraction_ring LinearIndependent.iff_fractionRingₓ'. -/
 theorem LinearIndependent.iff_fractionRing {ι : Type _} {b : ι → V} :
     LinearIndependent R b ↔ LinearIndependent K b :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu, Anne Baanen
 
 ! This file was ported from Lean 3 source module ring_theory.localization.module
-! leanprover-community/mathlib commit 2e59a6de168f95d16b16d217b808a36290398c0a
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Localization.Integer
 /-!
 # Modules / vector spaces over localizations / fraction fields
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains some results about vector spaces over the field of fractions of a ring.
 
 ## Main results

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

@@ -44,6 +44,12 @@ section AddCommMonoid
 
 variable {M : Type _} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
 
+/- warning: linear_independent.localization -> LinearIndependent.localization is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {M : Type.{u3}} [_inst_4 : AddCommMonoid.{u3} M] [_inst_5 : Module.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4] [_inst_6 : Module.{u2, u3} Rₛ M (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4] [_inst_7 : IsScalarTower.{u1, u2, u3} R Rₛ M (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} Rₛ M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u2, u3} Rₛ M (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u2, u3} Rₛ M (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u2, u3} Rₛ M (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4 _inst_6)))) (SMulZeroClass.toHasSmul.{u1, u3} R M (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (SMulWithZero.toSmulZeroClass.{u1, u3} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (MulActionWithZero.toSMulWithZero.{u1, u3} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} M (AddMonoid.toAddZeroClass.{u3} M (AddCommMonoid.toAddMonoid.{u3} M _inst_4))) (Module.toMulActionWithZero.{u1, u3} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_5))))] {ι : Type.{u4}} {b : ι -> M}, (LinearIndependent.{u4, u1, u3} ι R M b (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) _inst_4 _inst_5) -> (LinearIndependent.{u4, u2, u3} ι Rₛ M b (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_4 _inst_6)
+but is expected to have type
+  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {M : Type.{u2}} [_inst_4 : AddCommMonoid.{u2} M] [_inst_5 : Module.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) _inst_4] [_inst_6 : Module.{u1, u2} Rₛ M (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_4] [_inst_7 : IsScalarTower.{u3, u1, u2} R Rₛ M (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_3) (SMulZeroClass.toSMul.{u1, u2} Rₛ M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u1, u2} Rₛ M (CommMonoidWithZero.toZero.{u1} Rₛ (CommSemiring.toCommMonoidWithZero.{u1} Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u1, u2} Rₛ M (Semiring.toMonoidWithZero.{u1} Rₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u1, u2} Rₛ M (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_4 _inst_6)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_4)) (Module.toMulActionWithZero.{u3, u2} R M (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) _inst_4 _inst_5))))] {ι : Type.{u4}} {b : ι -> M}, (LinearIndependent.{u4, u3, u2} ι R M b (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) _inst_4 _inst_5) -> (LinearIndependent.{u4, u1, u2} ι Rₛ M b (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_4 _inst_6)
+Case conversion may be inaccurate. Consider using '#align linear_independent.localization LinearIndependent.localizationₓ'. -/
 theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
   rw [linearIndependent_iff'] at hli⊢
@@ -74,6 +80,12 @@ include hA
 
 open Submodule
 
+/- warning: linear_independent.localization_localization -> LinearIndependent.localization_localization is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u1, u3} ι R A v (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u4} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u4} ι A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))
+but is expected to have type
+  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} {v : ι -> A}, (LinearIndependent.{u5, u4, u3} ι R A v (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) -> (LinearIndependent.{u5, u2, u1} ι Rₛ Aₛ (Function.comp.{succ u5, succ u3, succ u1} ι A Aₛ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7)) v) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8))
+Case conversion may be inaccurate. Consider using '#align linear_independent.localization_localization LinearIndependent.localization_localizationₓ'. -/
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) :=
   by
@@ -96,6 +108,12 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
   exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨⟨r, hrS⟩, hv⟩
 #align linear_independent.localization_localization LinearIndependent.localization_localization
 
+/- warning: span_eq_top.localization_localization -> SpanEqTop.localization_localization is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {v : Set.{u3} A}, (Eq.{succ u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.span.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) v) (Top.top.{u3} (Submodule.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Submodule.hasTop.{u1, u3} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)))) -> (Eq.{succ u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Set.image.{u3, u4} A Aₛ (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u4} (Submodule.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (Submodule.hasTop.{u2, u4} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))
+but is expected to have type
+  forall {R : Type.{u3}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))] (S : Submonoid.{u3} R (MulZeroOneClass.toMulOneClass.{u3} R (NonAssocSemiring.toMulZeroOneClass.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (CommRing.toRing.{u3} R _inst_1)))))) [hT : IsLocalization.{u3, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u4}} [_inst_4 : CommRing.{u4} A] [_inst_5 : Algebra.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u3, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u3, u1} R Rₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u3, u4, u2} R A Aₛ (Algebra.toSMul.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5) (Algebra.toSMul.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u3, u2} R Aₛ (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u4, u2} A (CommRing.toCommSemiring.{u4} A _inst_4) (Algebra.algebraMapSubmonoid.{u3, u4} R (CommRing.toCommSemiring.{u3} R _inst_1) A (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {v : Set.{u4} A}, (Eq.{succ u4} (Submodule.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5)) (Submodule.span.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5) v) (Top.top.{u4} (Submodule.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5)) (Submodule.instTopSubmodule.{u3, u4} R A (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u4} A (NonAssocRing.toNonUnitalNonAssocRing.{u4} A (Ring.toNonAssocRing.{u4} A (CommRing.toRing.{u4} A _inst_4))))) (Algebra.toModule.{u3, u4} R A (CommRing.toCommSemiring.{u3} R _inst_1) (Ring.toSemiring.{u4} A (CommRing.toRing.{u4} A _inst_4)) _inst_5)))) -> (Eq.{succ u2} (Submodule.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.span.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8) (Set.image.{u4, u2} A Aₛ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u4, u2} A Aₛ (Semiring.toNonAssocSemiring.{u4} A (CommSemiring.toSemiring.{u4} A (CommRing.toCommSemiring.{u4} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))))) (algebraMap.{u4, u2} A Aₛ (CommRing.toCommSemiring.{u4} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7)) v)) (Top.top.{u2} (Submodule.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) (Submodule.instTopSubmodule.{u1, u2} Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8))))
+Case conversion may be inaccurate. Consider using '#align span_eq_top.localization_localization SpanEqTop.localization_localizationₓ'. -/
 theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
   rw [eq_top_iff]
@@ -112,6 +130,7 @@ theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
   · infer_instance
 #align span_eq_top.localization_localization SpanEqTop.localization_localization
 
+#print Basis.localizationLocalization /-
 /-- If `A` has an `R`-basis, then localizing `A` at `S` has a basis over `R` localized at `S`.
 
 A suitable instance for `[algebra A Aₛ]` is `localization_algebra`.
@@ -122,13 +141,26 @@ noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A
       rw [Set.range_comp, SpanEqTop.localization_localization Rₛ S Aₛ b.span_eq]
       exact le_rfl)
 #align basis.localization_localization Basis.localizationLocalization
+-/
 
+/- warning: basis.localization_localization_apply -> Basis.localizationLocalization_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u4} Aₛ (coeFn.{max (succ u5) (succ u2) (succ u4), max (succ u5) (succ u4)} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) (fun (_x : Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) => ι -> Aₛ) (FunLike.hasCoeToFun.{max (succ u5) (succ u2) (succ u4), succ u5, succ u4} (Basis.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => Aₛ) (Basis.funLike.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) (coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (fun (_x : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) => ι -> A) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => A) (Basis.funLike.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))) b i))
+but is expected to have type
+  forall {R : Type.{u4}} (Rₛ : Type.{u1}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u1} Rₛ] [_inst_3 : Algebra.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u1} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u2}) [_inst_6 : CommRing.{u2} Aₛ] [_inst_7 : Algebra.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_8 : Algebra.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u1, u2} R Rₛ Aₛ (Algebra.toSMul.{u4, u1} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u2} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u2} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u2} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u2} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) i) (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u5), succ u5, succ u2} (Basis.{u5, u1, u2} ι Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => Aₛ) _x) (Basis.funLike.{u5, u1, u2} ι Rₛ Aₛ (Ring.toSemiring.{u1} Rₛ (CommRing.toRing.{u1} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u2} Aₛ (Ring.toNonAssocRing.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (Algebra.toModule.{u1, u2} Rₛ Aₛ (CommRing.toCommSemiring.{u1} Rₛ _inst_2) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_8)) (Basis.localizationLocalization.{u4, u1, u3, u2, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b) i) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u2} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Aₛ (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u2} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u2} Aₛ (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6))))))) (algebraMap.{u3, u2} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u2} Aₛ (CommRing.toRing.{u2} Aₛ _inst_6)) _inst_7) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u5, succ u3} (Basis.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => A) _x) (Basis.funLike.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) b i))
+Case conversion may be inaccurate. Consider using '#align basis.localization_localization_apply Basis.localizationLocalization_applyₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
     b.localization_localization Rₛ S Aₛ i = algebraMap A Aₛ (b i) :=
   Basis.mk_apply _ _ _
 #align basis.localization_localization_apply Basis.localizationLocalization_apply
 
+/- warning: basis.localization_localization_repr_algebra_map -> Basis.localizationLocalization_repr_algebraMap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (NonAssocSemiring.toMulZeroOneClass.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) [hT : IsLocalization.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u4}) [_inst_6 : CommRing.{u4} Aₛ] [_inst_7 : Algebra.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_9 : Algebra.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u1, u2, u4} R Rₛ Aₛ (SMulZeroClass.toHasSmul.{u1, u2} R Rₛ (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R Rₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R Rₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} Rₛ (AddMonoid.toAddZeroClass.{u2} Rₛ (AddCommMonoid.toAddMonoid.{u2} Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R Rₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Algebra.toModule.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u4} Rₛ Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u2, u4} Rₛ Aₛ (MulZeroClass.toHasZero.{u2} Rₛ (MulZeroOneClass.toMulZeroClass.{u2} Rₛ (MonoidWithZero.toMulZeroOneClass.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u2, u4} Rₛ Aₛ (Semiring.toMonoidWithZero.{u2} Rₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u2, u4} Rₛ Aₛ (CommSemiring.toSemiring.{u2} Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [_inst_11 : IsScalarTower.{u1, u3, u4} R A Aₛ (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toHasSmul.{u3, u4} A Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u3, u4} A Aₛ (MulZeroClass.toHasZero.{u3} A (MulZeroOneClass.toMulZeroClass.{u3} A (MonoidWithZero.toMulZeroOneClass.{u3} A (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u3, u4} A Aₛ (Semiring.toMonoidWithZero.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u3, u4} A Aₛ (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7))))) (SMulZeroClass.toHasSmul.{u1, u4} R Aₛ (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R Aₛ (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R Aₛ (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u4} Aₛ (AddMonoid.toAddZeroClass.{u4} Aₛ (AddCommMonoid.toAddMonoid.{u4} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))))))) (Module.toMulActionWithZero.{u1, u4} R Aₛ (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} Aₛ (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u1, u4} R Aₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_9)))))] [hA : IsLocalization.{u3, u4} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u1, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u4} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} Rₛ (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (fun (_x : Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) => ι -> Rₛ) (Finsupp.coeFun.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (coeFn.{max (succ u4) (succ (max u5 u2)), max (succ u4) (succ (max u5 u2))} (LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (fun (_x : LinearEquiv.{u2, u2, u4, max u5 u2} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) => Aₛ -> (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (LinearEquiv.hasCoeToFun.{u2, u2, u4, max u5 u2} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MulZeroClass.toHasZero.{u2} Rₛ (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (Basis.repr.{u5, u2, u4} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} Aₛ (NonUnitalNonAssocRing.toAddCommGroup.{u4} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u4} Aₛ (Ring.toNonAssocRing.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6))))) (Algebra.toModule.{u2, u4} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u1, u2, u3, u4, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (fun (_x : RingHom.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) => A -> Aₛ) (RingHom.hasCoeToFun.{u3, u4} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u4} Aₛ (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)))) (algebraMap.{u3, u4} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u4} Aₛ (CommRing.toRing.{u4} Aₛ _inst_6)) _inst_7) x)) i) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (fun (_x : RingHom.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) => R -> Rₛ) (RingHom.hasCoeToFun.{u1, u2} R Rₛ (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (algebraMap.{u1, u2} R Rₛ (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (coeFn.{max (succ u5) (succ u1), max (succ u5) (succ u1)} (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (fun (_x : Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) => ι -> R) (Finsupp.coeFun.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (coeFn.{max (succ u3) (succ (max u5 u1)), max (succ u3) (succ (max u5 u1))} (LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u3, max u5 u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => A -> (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max u5 u1} R R A (Finsupp.{u5, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u1, u1} ι R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Basis.repr.{u5, u1, u3} ι R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toAddCommGroup.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u1, u3} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) b) x) i))
+but is expected to have type
+  forall {R : Type.{u4}} (Rₛ : Type.{u2}) [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u2} Rₛ] [_inst_3 : Algebra.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))] (S : Submonoid.{u4} R (MulZeroOneClass.toMulOneClass.{u4} R (NonAssocSemiring.toMulZeroOneClass.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) [hT : IsLocalization.{u4, u2} R (CommRing.toCommSemiring.{u4} R _inst_1) S Rₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) _inst_3] {A : Type.{u3}} [_inst_4 : CommRing.{u3} A] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4))] (Aₛ : Type.{u1}) [_inst_6 : CommRing.{u1} Aₛ] [_inst_7 : Algebra.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_8 : Algebra.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_9 : Algebra.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))] [_inst_10 : IsScalarTower.{u4, u2, u1} R Rₛ Aₛ (Algebra.toSMul.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (Algebra.toSMul.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [_inst_11 : IsScalarTower.{u4, u3, u1} R A Aₛ (Algebra.toSMul.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Algebra.toSMul.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7) (Algebra.toSMul.{u4, u1} R Aₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_9)] [hA : IsLocalization.{u3, u1} A (CommRing.toCommSemiring.{u3} A _inst_4) (Algebra.algebraMapSubmonoid.{u4, u3} R (CommRing.toCommSemiring.{u4} R _inst_1) A (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5 S) Aₛ (CommRing.toCommSemiring.{u1} Aₛ _inst_6) _inst_7] {ι : Type.{u5}} (b : Basis.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (x : A) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) i) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => Rₛ) _x) (Finsupp.funLike.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u5), succ u1, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) Aₛ (fun (_x : Aₛ) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Aₛ) => Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) _x) (SMulHomClass.toFunLike.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} Rₛ Aₛ (AddMonoid.toZero.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribSMul.toSMulZeroClass.{u2, u1} Rₛ Aₛ (AddMonoid.toAddZeroClass.{u1} Aₛ (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (DistribMulAction.toDistribSMul.{u2, u1} Rₛ Aₛ (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8))))) (SMulZeroClass.toSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u1) u5, u2, u1, max u2 u5} (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (MonoidWithZero.toMonoid.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (AddCommMonoid.toAddMonoid.{u1} Aₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (Module.toDistribMulAction.{u2, u1} Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8)) (Module.toDistribMulAction.{u2, max u2 u5} Rₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (SemilinearMapClass.distribMulActionHomClass.{u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u1, max u2 u5, max (max u2 u1) u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (LinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u1, max u2 u5} Rₛ Rₛ Aₛ (Finsupp.{u5, u2} ι Rₛ (MonoidWithZero.toZero.{u2} Rₛ (Semiring.toMonoidWithZero.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Finsupp.addCommMonoid.{u5, u2} ι Rₛ (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Finsupp.module.{u5, u2, u2} ι Rₛ Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (Semiring.toModule.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHom.id.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHomInvPair.ids.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))))))) (Basis.repr.{u5, u2, u1} ι Rₛ Aₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} Aₛ (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} Aₛ (NonAssocRing.toNonUnitalNonAssocRing.{u1} Aₛ (Ring.toNonAssocRing.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (Algebra.toModule.{u2, u1} Rₛ Aₛ (CommRing.toCommSemiring.{u2} Rₛ _inst_2) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_8) (Basis.localizationLocalization.{u4, u2, u3, u1, u5} R Rₛ _inst_1 _inst_2 _inst_3 S hT A _inst_4 _inst_5 Aₛ _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 hA ι b)) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => Aₛ) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} Aₛ (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)))) A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))) (RingHom.instRingHomClassRingHom.{u3, u1} A Aₛ (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_4))) (Semiring.toNonAssocSemiring.{u1} Aₛ (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6))))))) (algebraMap.{u3, u1} A Aₛ (CommRing.toCommSemiring.{u3} A _inst_4) (Ring.toSemiring.{u1} Aₛ (CommRing.toRing.{u1} Aₛ _inst_6)) _inst_7) x)) i) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Rₛ) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R Rₛ (NonUnitalNonAssocSemiring.toMul.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u2} Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R Rₛ (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} Rₛ (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u4 u2, u4, u2} (RingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)))) R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))) (RingHom.instRingHomClassRingHom.{u4, u2} R Rₛ (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} Rₛ (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2))))))) (algebraMap.{u4, u2} R Rₛ (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u2} Rₛ (CommRing.toRing.{u2} Rₛ _inst_2)) _inst_3) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (FunLike.coe.{max (max (succ u4) (succ u3)) (succ u5), succ u3, max (succ u4) (succ u5)} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) _x) (SMulHomClass.toFunLike.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (SMulZeroClass.toSMul.{u4, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u3} R A (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (Module.toDistribMulAction.{u4, u3} R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5))))) (SMulZeroClass.toSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddMonoid.toZero.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddMonoid.toAddZeroClass.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u4 u3) u5, u4, u3, max u4 u5} (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4)))))) (AddCommMonoid.toAddMonoid.{max u4 u5} (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))))) (Module.toDistribMulAction.{u4, u3} R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5)) (Module.toDistribMulAction.{u4, max u4 u5} R (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u4, u3, max u4 u5, max (max u4 u3) u5} R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u4, u4, u3, max u4 u5, max (max u4 u3) u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (LinearEquiv.{u4, u4, u3, max u4 u5} R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u4, u4, u3, max u4 u5} R R A (Finsupp.{u5, u4} ι R (MonoidWithZero.toZero.{u4} R (Semiring.toMonoidWithZero.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Finsupp.addCommMonoid.{u5, u4} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) (Finsupp.module.{u5, u4, u4} ι R R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))))) (Semiring.toModule.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1))) (RingHomInvPair.ids.{u4} R (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)))))))) (Basis.repr.{u5, u4, u3} ι R A (Ring.toSemiring.{u4} R (CommRing.toRing.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} A (NonAssocRing.toNonUnitalNonAssocRing.{u3} A (Ring.toNonAssocRing.{u3} A (CommRing.toRing.{u3} A _inst_4))))) (Algebra.toModule.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (Ring.toSemiring.{u3} A (CommRing.toRing.{u3} A _inst_4)) _inst_5) b) x) i))
+Case conversion may be inaccurate. Consider using '#align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMapₓ'. -/
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :
     (b.localization_localization Rₛ S Aₛ).repr (algebraMap A Aₛ x) i =
@@ -161,11 +193,17 @@ variable (R K : Type _) [CommRing R] [Field K] [Algebra R K] [IsFractionRing R K
 
 variable {V : Type _} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
 
-theorem LinearIndependent.iff_fraction_ring {ι : Type _} {b : ι → V} :
+/- warning: linear_independent.iff_fraction_ring -> LinearIndependent.iff_fractionRing is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (K : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : Field.{u2} K] [_inst_3 : Algebra.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))] [_inst_4 : IsFractionRing.{u1, u2} R _inst_1 K (Field.toCommRing.{u2} K _inst_2) _inst_3] {V : Type.{u3}} [_inst_5 : AddCommGroup.{u3} V] [_inst_6 : Module.{u1, u3} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)] [_inst_7 : Module.{u2, u3} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)] [_inst_8 : IsScalarTower.{u1, u2, u3} R K V (SMulZeroClass.toHasSmul.{u1, u2} R K (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R K (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R K (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} K (AddMonoid.toAddZeroClass.{u2} K (AddCommMonoid.toAddMonoid.{u2} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))))) (Module.toMulActionWithZero.{u1, u2} R K (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} K (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Algebra.toModule.{u1, u2} R K (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} K V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u2, u3} K V (MulZeroClass.toHasZero.{u2} K (MulZeroOneClass.toMulZeroClass.{u2} K (MonoidWithZero.toMulZeroOneClass.{u2} K (Semiring.toMonoidWithZero.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u2, u3} K V (Semiring.toMonoidWithZero.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (Module.toMulActionWithZero.{u2, u3} K V (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_7)))) (SMulZeroClass.toHasSmul.{u1, u3} R V (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (SMulWithZero.toSmulZeroClass.{u1, u3} R V (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (MulActionWithZero.toSMulWithZero.{u1, u3} R V (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} V (AddMonoid.toAddZeroClass.{u3} V (AddCommMonoid.toAddMonoid.{u3} V (AddCommGroup.toAddCommMonoid.{u3} V _inst_5)))) (Module.toMulActionWithZero.{u1, u3} R V (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_6))))] {ι : Type.{u4}} {b : ι -> V}, Iff (LinearIndependent.{u4, u1, u3} ι R V b (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_6) (LinearIndependent.{u4, u2, u3} ι K V b (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V _inst_5) _inst_7)
+but is expected to have type
+  forall (R : Type.{u3}) (K : Type.{u1}) [_inst_1 : CommRing.{u3} R] [_inst_2 : Field.{u1} K] [_inst_3 : Algebra.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))] [_inst_4 : IsFractionRing.{u3, u1} R _inst_1 K (Field.toCommRing.{u1} K _inst_2) _inst_3] {V : Type.{u2}} [_inst_5 : AddCommGroup.{u2} V] [_inst_6 : Module.{u3, u2} R V (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_7 : Module.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5)] [_inst_8 : IsScalarTower.{u3, u1, u2} R K V (Algebra.toSMul.{u3, u1} R K (CommRing.toCommSemiring.{u3} R _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) _inst_3) (SMulZeroClass.toSMul.{u1, u2} K V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u1, u2} K V (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u1, u2} K V (Semiring.toMonoidWithZero.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u1, u2} K V (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)))) (SMulZeroClass.toSMul.{u3, u2} R V (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (SMulWithZero.toSMulZeroClass.{u3, u2} R V (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (MulActionWithZero.toSMulWithZero.{u3, u2} R V (Semiring.toMonoidWithZero.{u3} R (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V _inst_5))))) (Module.toMulActionWithZero.{u3, u2} R V (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6))))] {ι : Type.{u4}} {b : ι -> V}, Iff (LinearIndependent.{u4, u3, u2} ι R V b (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_6) (LinearIndependent.{u4, u1, u2} ι K V b (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} V _inst_5) _inst_7)
+Case conversion may be inaccurate. Consider using '#align linear_independent.iff_fraction_ring LinearIndependent.iff_fractionRingₓ'. -/
+theorem LinearIndependent.iff_fractionRing {ι : Type _} {b : ι → V} :
     LinearIndependent R b ↔ LinearIndependent K b :=
   ⟨LinearIndependent.localization K R⁰,
     LinearIndependent.restrict_scalars (smul_left_injective R one_ne_zero)⟩
-#align linear_independent.iff_fraction_ring LinearIndependent.iff_fraction_ring
+#align linear_independent.iff_fraction_ring LinearIndependent.iff_fractionRing
 
 end FractionRing
 

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

@@ -145,8 +145,8 @@ theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis
       simp_rw [← b.localization_localization_apply Rₛ S Aₛ, map_finsupp_sum, LinearEquiv.map_smul,
         Basis.repr_self, Finsupp.sum_apply, Finsupp.smul_apply]
     _ = _ :=
-      Finset.sum_eq_single i (fun j _ hj => by simp [hj]) fun hi => by
-        simp [finsupp.not_mem_support_iff.mp hi]
+      (Finset.sum_eq_single i (fun j _ hj => by simp [hj]) fun hi => by
+        simp [finsupp.not_mem_support_iff.mp hi])
     _ = algebraMap R Rₛ (b.repr x i) := by simp [Algebra.smul_def]
     
 #align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMap

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -42,7 +42,6 @@ section AddCommMonoid
 open Submodule
 
 variable [CommSemiring Rₛ] [Algebra R Rₛ] [hT : IsLocalization S Rₛ]
-
 variable {M M' : Type*} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
   [AddCommMonoid M'] [Module R M'] [Module Rₛ M'] [IsScalarTower R Rₛ M'] (f : M →ₗ[R] M')
   [IsLocalizedModule S f]
@@ -126,15 +125,10 @@ end IsLocalizedModule
 section LocalizationLocalization
 
 variable {R : Type*} (Rₛ : Type*) [CommSemiring R] [CommRing Rₛ] [Algebra R Rₛ]
-
 variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
-
 variable {A : Type*} [CommRing A] [Algebra R A]
-
 variable (Aₛ : Type*) [CommRing Aₛ] [Algebra A Aₛ]
-
 variable [Algebra Rₛ Aₛ] [Algebra R Aₛ] [IsScalarTower R Rₛ Aₛ] [IsScalarTower R A Aₛ]
-
 variable [hA : IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ]
 
 open Submodule
@@ -179,7 +173,6 @@ end LocalizationLocalization
 section FractionRing
 
 variable (R K : Type*) [CommRing R] [Field K] [Algebra R K] [IsFractionRing R K]
-
 variable {V : Type*} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
 
 theorem LinearIndependent.iff_fractionRing {ι : Type*} {b : ι → V} :

See this Zulip discussion.

@@ -137,8 +137,6 @@ variable [Algebra Rₛ Aₛ] [Algebra R Aₛ] [IsScalarTower R Rₛ Aₛ] [IsSca
 
 variable [hA : IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ]
 
---include hA
-
 open Submodule
 
 theorem LinearIndependent.localization_localization {ι : Type*} {v : ι → A}

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -105,7 +105,7 @@ theorem Basis.ofIsLocalizedModule_repr_apply (m : M) (i : ι) :
     ((b.ofIsLocalizedModule Rₛ S f).repr (f m)) i = algebraMap R Rₛ (b.repr m i) := by
   suffices ((b.ofIsLocalizedModule Rₛ S f).repr.toLinearMap.restrictScalars R) ∘ₗ f =
       Finsupp.mapRange.linearMap (Algebra.linearMap R Rₛ) ∘ₗ b.repr.toLinearMap by
-    exact FunLike.congr_fun (LinearMap.congr_fun this m) i
+    exact DFunLike.congr_fun (LinearMap.congr_fun this m) i
   refine Basis.ext b fun i ↦ ?_
   rw [LinearMap.coe_comp, Function.comp_apply, LinearMap.coe_restrictScalars,
     LinearEquiv.coe_coe, ← b.ofIsLocalizedModule_apply Rₛ S f, repr_self, LinearMap.coe_comp,

@@ -35,8 +35,6 @@ section Localization
 
 variable {R : Type*} (Rₛ : Type*) [CommSemiring R] (S : Submonoid R)
 
--- include hT
-
 section IsLocalizedModule
 
 section AddCommMonoid
@@ -95,8 +93,8 @@ variable {M Mₛ : Type*} [AddCommGroup M] [AddCommGroup Mₛ] [Module R M] [Mod
 
 /-- If `M` has an `R`-basis, then localizing `M` at `S` has a basis over `R` localized at `S`. -/
 noncomputable def Basis.ofIsLocalizedModule : Basis ι Rₛ Mₛ :=
-  Basis.mk (b.linearIndependent.of_isLocalizedModule Rₛ S f)
-  (by rw [Set.range_comp, span_eq_top_of_isLocalizedModule Rₛ S _ b.span_eq])
+  .mk (b.linearIndependent.of_isLocalizedModule Rₛ S f) <| by
+    rw [Set.range_comp, span_eq_top_of_isLocalizedModule Rₛ S _ b.span_eq]
 
 @[simp]
 theorem Basis.ofIsLocalizedModule_apply (i : ι) : b.ofIsLocalizedModule Rₛ S f i = f (b i) := by

Let Mₛ be a R-module and let M be a submodule of Mₛ such that Mₛ is the localization at S of M where S is a submonoid of R. Assume that Mₛ is a Rₛ-module where Rₛ is a localization of R at S. Then, any R-basis of M is a Rₛ-basis of Mₛ.

This result is used to prove the results about Basis.localizationLocalization. For that, it is necessary to move some results between files and modify some imports.

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

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

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu, Anne Baanen
 -/
 import Mathlib.LinearAlgebra.Basis
+import Mathlib.Algebra.Module.LocalizedModule
 import Mathlib.RingTheory.Localization.FractionRing
 import Mathlib.RingTheory.Localization.Integer
 
@@ -18,8 +19,9 @@ This file contains some results about vector spaces over the field of fractions
 
  * `LinearIndependent.localization`: `b` is linear independent over a localization of `R`
    if it is linear independent over `R` itself
- * `Basis.localizationLocalization`: promote an `R`-basis `b` of `A` to an `Rₛ`-basis of `Aₛ`,
-   where `Rₛ` and `Aₛ` are localizations of `R` and `A` at `s` respectively
+ * `Basis.ofIsLocalizedModule` / `Basis.localizationLocalization`: promote an `R`-basis `b` of `A`
+   to an `Rₛ`-basis of `Aₛ`, where `Rₛ` and `Aₛ` are localizations of `R` and `A` at `s`
+   respectively
  * `LinearIndependent.iff_fractionRing`: `b` is linear independent over `R` iff it is
    linear independent over `Frac(R)`
 -/
@@ -31,35 +33,101 @@ open nonZeroDivisors
 
 section Localization
 
-variable {R : Type*} (Rₛ : Type*) [CommSemiring R] [CommSemiring Rₛ] [Algebra R Rₛ]
-
-variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
+variable {R : Type*} (Rₛ : Type*) [CommSemiring R] (S : Submonoid R)
 
 -- include hT
 
+section IsLocalizedModule
+
 section AddCommMonoid
 
-variable {M : Type*} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
+open Submodule
+
+variable [CommSemiring Rₛ] [Algebra R Rₛ] [hT : IsLocalization S Rₛ]
+
+variable {M M' : Type*} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
+  [AddCommMonoid M'] [Module R M'] [Module Rₛ M'] [IsScalarTower R Rₛ M'] (f : M →ₗ[R] M')
+  [IsLocalizedModule S f]
+
+theorem span_eq_top_of_isLocalizedModule {v : Set M} (hv : span R v = ⊤) :
+    span Rₛ (f '' v) = ⊤ := top_unique fun x _ ↦ by
+  obtain ⟨⟨m, s⟩, h⟩ := IsLocalizedModule.surj S f x
+  rw [Submonoid.smul_def, ← algebraMap_smul Rₛ, ← Units.smul_isUnit (IsLocalization.map_units Rₛ s),
+    eq_comm, ← inv_smul_eq_iff] at h
+  refine h ▸ smul_mem _ _  (span_subset_span R Rₛ _ ?_)
+  rw [← LinearMap.coe_restrictScalars R, ← LinearMap.map_span, hv]
+  exact mem_map_of_mem mem_top
+
+theorem LinearIndependent.of_isLocalizedModule {ι : Type*} {v : ι → M}
+    (hv : LinearIndependent R v) : LinearIndependent Rₛ (f ∘ v) := by
+  rw [linearIndependent_iff'] at hv ⊢
+  intro t g hg i hi
+  choose! a g' hg' using IsLocalization.exist_integer_multiples S t g
+  have h0 : f (∑ i in t, g' i • v i) = 0 := by
+    apply_fun ((a : R) • ·) at hg
+    rw [smul_zero, Finset.smul_sum] at hg
+    rw [map_sum, ← hg]
+    refine Finset.sum_congr rfl fun i hi => ?_
+    rw [← smul_assoc, ← hg' i hi, map_smul, Function.comp_apply, algebraMap_smul]
+  obtain ⟨s, hs⟩ := (IsLocalizedModule.eq_zero_iff S f).mp h0
+  simp_rw [Finset.smul_sum, Submonoid.smul_def, smul_smul] at hs
+  specialize hv t _ hs i hi
+  rw [← (IsLocalization.map_units Rₛ a).mul_right_eq_zero, ← Algebra.smul_def, ← hg' i hi]
+  exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨s, hv⟩
 
 theorem LinearIndependent.localization {ι : Type*} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
-  rw [linearIndependent_iff'] at hli ⊢
-  intro s g hg i hi
-  choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
-  specialize hli s g' _ i hi
-  · rw [← @smul_zero _ M _ _ (a : R), ← hg, Finset.smul_sum]
-    refine' Finset.sum_congr rfl fun i hi => _
-    rw [← IsScalarTower.algebraMap_smul Rₛ, hg' i hi, smul_assoc]
-  refine' (IsLocalization.map_units Rₛ a).mul_right_eq_zero.mp _
-  rw [← Algebra.smul_def, ← map_zero (algebraMap R Rₛ), ← hli, hg' i hi]
+  have := isLocalizedModule_id S M Rₛ
+  exact hli.of_isLocalizedModule Rₛ S .id
 #align linear_independent.localization LinearIndependent.localization
 
 end AddCommMonoid
-end Localization
+
+section Basis
+
+variable [CommRing Rₛ] [Algebra R Rₛ] [hT : IsLocalization S Rₛ]
+
+open Submodule
+
+variable {M Mₛ : Type*} [AddCommGroup M] [AddCommGroup Mₛ] [Module R M] [Module R Mₛ] [Module R Mₛ]
+  [Module Rₛ Mₛ] (f : M →ₗ[R] Mₛ) [IsLocalizedModule S f] [IsScalarTower R Rₛ Mₛ]
+  {ι : Type*} (b : Basis ι R M)
+
+/-- If `M` has an `R`-basis, then localizing `M` at `S` has a basis over `R` localized at `S`. -/
+noncomputable def Basis.ofIsLocalizedModule : Basis ι Rₛ Mₛ :=
+  Basis.mk (b.linearIndependent.of_isLocalizedModule Rₛ S f)
+  (by rw [Set.range_comp, span_eq_top_of_isLocalizedModule Rₛ S _ b.span_eq])
+
+@[simp]
+theorem Basis.ofIsLocalizedModule_apply (i : ι) : b.ofIsLocalizedModule Rₛ S f i = f (b i) := by
+  rw [ofIsLocalizedModule, coe_mk, Function.comp_apply]
+
+@[simp]
+theorem Basis.ofIsLocalizedModule_repr_apply (m : M) (i : ι) :
+    ((b.ofIsLocalizedModule Rₛ S f).repr (f m)) i = algebraMap R Rₛ (b.repr m i) := by
+  suffices ((b.ofIsLocalizedModule Rₛ S f).repr.toLinearMap.restrictScalars R) ∘ₗ f =
+      Finsupp.mapRange.linearMap (Algebra.linearMap R Rₛ) ∘ₗ b.repr.toLinearMap by
+    exact FunLike.congr_fun (LinearMap.congr_fun this m) i
+  refine Basis.ext b fun i ↦ ?_
+  rw [LinearMap.coe_comp, Function.comp_apply, LinearMap.coe_restrictScalars,
+    LinearEquiv.coe_coe, ← b.ofIsLocalizedModule_apply Rₛ S f, repr_self, LinearMap.coe_comp,
+    Function.comp_apply, LinearEquiv.coe_coe, repr_self, Finsupp.mapRange.linearMap_apply,
+    Finsupp.mapRange_single, Algebra.linearMap_apply, map_one]
+
+theorem Basis.ofIsLocalizedModule_span :
+    span R (Set.range (b.ofIsLocalizedModule Rₛ S f)) = LinearMap.range f := by
+  calc span R (Set.range (b.ofIsLocalizedModule Rₛ S f))
+    _ = span R (f '' (Set.range b)) := by congr; ext; simp
+    _ = map f (span R (Set.range b)) := by rw [Submodule.map_span]
+    _ = LinearMap.range f := by rw [b.span_eq, Submodule.map_top]
+
+end Basis
+
+end IsLocalizedModule
 
 section LocalizationLocalization
 
-variable {R : Type*} (Rₛ : Type*) [CommRing R] [CommRing Rₛ] [Algebra R Rₛ]
+variable {R : Type*} (Rₛ : Type*) [CommSemiring R] [CommRing Rₛ] [Algebra R Rₛ]
 
 variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
 
@@ -76,82 +144,38 @@ variable [hA : IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ]
 open Submodule
 
 theorem LinearIndependent.localization_localization {ι : Type*} {v : ι → A}
-    (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) := by
-  rw [linearIndependent_iff'] at hv ⊢
-  intro s g hg i hi
-  choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
-  have h0 : algebraMap A Aₛ (∑ i in s, g' i • v i) = 0 := by
-    apply_fun ((a : R) • ·) at hg
-    rw [smul_zero, Finset.smul_sum] at hg
-    rw [map_sum, ← hg]
-    refine' Finset.sum_congr rfl fun i hi => _
-    rw [← smul_assoc, ← hg' i hi, Algebra.smul_def, map_mul, ← IsScalarTower.algebraMap_apply, ←
-      Algebra.smul_def, algebraMap_smul, Function.comp_apply]
-  obtain ⟨⟨_, r, hrS, rfl⟩, hr : algebraMap R A r * _ = 0⟩ :=
-    (IsLocalization.map_eq_zero_iff (Algebra.algebraMapSubmonoid A S) _ _).1 h0
-  simp_rw [Finset.mul_sum, ← Algebra.smul_def, smul_smul] at hr
-  specialize hv s _ hr i hi
-  rw [← (IsLocalization.map_units Rₛ a).mul_right_eq_zero, ← Algebra.smul_def, ← hg' i hi]
-  exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨⟨r, hrS⟩, hv⟩
+    (hv : LinearIndependent R v) : LinearIndependent Rₛ ((algebraMap A Aₛ) ∘ v) :=
+  hv.of_isLocalizedModule Rₛ S (IsScalarTower.toAlgHom R A Aₛ).toLinearMap
 #align linear_independent.localization_localization LinearIndependent.localization_localization
 
-theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
-    span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
-  rw [eq_top_iff]
-  rintro a' -
-  obtain ⟨a, ⟨_, s, hs, rfl⟩, rfl⟩ :=
-    IsLocalization.mk'_surjective (Algebra.algebraMapSubmonoid A S) a'
-  rw [IsLocalization.mk'_eq_mul_mk'_one, mul_comm, ← map_one (algebraMap R A)]
-  erw [← IsLocalization.algebraMap_mk' A Rₛ Aₛ (1 : R) ⟨s, hs⟩]
-  -- `erw` needed to unify `⟨s, hs⟩`
-  rw [← Algebra.smul_def]
-  refine' smul_mem _ _ (span_subset_span R Rₛ _ _)
-  rw [← Algebra.coe_linearMap, ← LinearMap.coe_restrictScalars R, ← LinearMap.map_span]
-  exact mem_map_of_mem (hv.symm ▸ mem_top)
-#align span_eq_top.localization_localization SpanEqTop.localization_localization
+theorem span_eq_top_localization_localization {v : Set A} (hv : span R v = ⊤) :
+    span Rₛ (algebraMap A Aₛ '' v) = ⊤ :=
+  span_eq_top_of_isLocalizedModule Rₛ S (IsScalarTower.toAlgHom R A Aₛ).toLinearMap hv
+#align span_eq_top.localization_localization span_eq_top_localization_localization
 
 /-- If `A` has an `R`-basis, then localizing `A` at `S` has a basis over `R` localized at `S`.
 
 A suitable instance for `[Algebra A Aₛ]` is `localizationAlgebra`.
 -/
 noncomputable def Basis.localizationLocalization {ι : Type*} (b : Basis ι R A) : Basis ι Rₛ Aₛ :=
-  Basis.mk (b.linearIndependent.localization_localization _ S _)
-    (by rw [Set.range_comp, SpanEqTop.localization_localization Rₛ S Aₛ b.span_eq])
+  b.ofIsLocalizedModule Rₛ S (IsScalarTower.toAlgHom R A Aₛ).toLinearMap
 #align basis.localization_localization Basis.localizationLocalization
 
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type*} (b : Basis ι R A) (i) :
     b.localizationLocalization Rₛ S Aₛ i = algebraMap A Aₛ (b i) :=
-  Basis.mk_apply _ _ _
+  b.ofIsLocalizedModule_apply Rₛ S _ i
 #align basis.localization_localization_apply Basis.localizationLocalization_apply
 
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type*} (b : Basis ι R A) (x i) :
     (b.localizationLocalization Rₛ S Aₛ).repr (algebraMap A Aₛ x) i =
-      algebraMap R Rₛ (b.repr x i) :=
-  calc
-    (b.localizationLocalization Rₛ S Aₛ).repr (algebraMap A Aₛ x) i =
-        (b.localizationLocalization Rₛ S Aₛ).repr
-          ((b.repr x).sum fun j c => algebraMap R Rₛ c • algebraMap A Aₛ (b j)) i := by
-      simp_rw [IsScalarTower.algebraMap_smul, Algebra.smul_def,
-        IsScalarTower.algebraMap_apply R A Aₛ, ← _root_.map_mul, ← map_finsupp_sum, ←
-        Algebra.smul_def, ← Finsupp.total_apply, Basis.total_repr]
-    _ = (b.repr x).sum fun j c => algebraMap R Rₛ c • Finsupp.single j (1 : Rₛ) i := by
-      simp_rw [← b.localizationLocalization_apply Rₛ S Aₛ, map_finsupp_sum, LinearEquiv.map_smul,
-        Basis.repr_self, Finsupp.sum_apply, Finsupp.smul_apply]
-    _ = _ :=
-      (Finset.sum_eq_single i (fun j _ hj => by simp [hj]) fun hi => by
-        simp [Finsupp.not_mem_support_iff.mp hi])
-    _ = algebraMap R Rₛ (b.repr x i) := by simp [Algebra.smul_def]
+      algebraMap R Rₛ (b.repr x i) := b.ofIsLocalizedModule_repr_apply Rₛ S _ _ i
 #align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMap
 
 theorem Basis.localizationLocalization_span {ι : Type*} (b : Basis ι R A) :
     Submodule.span R (Set.range (b.localizationLocalization Rₛ S Aₛ)) =
-      LinearMap.range (IsScalarTower.toAlgHom R A Aₛ) :=
-  calc span R (Set.range ↑(localizationLocalization Rₛ S Aₛ b))
-    _ = span R (↑(IsScalarTower.toAlgHom R A Aₛ) '' Set.range ↑b) := by congr; ext; simp
-    _ = map (IsScalarTower.toAlgHom R A Aₛ) (span R (Set.range b)) := by rw [Submodule.map_span]
-    _ = LinearMap.range (IsScalarTower.toAlgHom R A Aₛ) := by rw [b.span_eq, Submodule.map_top]
+      LinearMap.range (IsScalarTower.toAlgHom R A Aₛ) := b.ofIsLocalizedModule_span Rₛ S _
 
 end LocalizationLocalization
 

Most of the changes are minor.

Co-authored-by: Xavier Xarles <56635243+XavierXarles@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -31,7 +31,7 @@ open nonZeroDivisors
 
 section Localization
 
-variable {R : Type*} (Rₛ : Type*) [CommRing R] [CommRing Rₛ] [Algebra R Rₛ]
+variable {R : Type*} (Rₛ : Type*) [CommSemiring R] [CommSemiring Rₛ] [Algebra R Rₛ]
 
 variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
 
@@ -55,9 +55,14 @@ theorem LinearIndependent.localization {ι : Type*} {b : ι → M} (hli : Linear
 #align linear_independent.localization LinearIndependent.localization
 
 end AddCommMonoid
+end Localization
 
 section LocalizationLocalization
 
+variable {R : Type*} (Rₛ : Type*) [CommRing R] [CommRing Rₛ] [Algebra R Rₛ]
+
+variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
+
 variable {A : Type*} [CommRing A] [Algebra R A]
 
 variable (Aₛ : Type*) [CommRing Aₛ] [Algebra A Aₛ]
@@ -150,7 +155,6 @@ theorem Basis.localizationLocalization_span {ι : Type*} (b : Basis ι R A) :
 
 end LocalizationLocalization
 
-end Localization
 
 section FractionRing
 
@@ -168,8 +172,8 @@ end FractionRing
 
 section
 
-variable {R : Type*} [CommRing R] (S : Submonoid R)
-variable (A : Type*) [CommRing A] [Algebra R A] [IsLocalization S A]
+variable {R : Type*} [CommSemiring R] (S : Submonoid R)
+variable (A : Type*) [CommSemiring A] [Algebra R A] [IsLocalization S A]
 variable {M N : Type*}
   [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
   [AddCommMonoid N] [Module R N] [Module A N] [IsScalarTower R A N]

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

@@ -76,7 +76,7 @@ theorem LinearIndependent.localization_localization {ι : Type*} {v : ι → A}
   intro s g hg i hi
   choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
   have h0 : algebraMap A Aₛ (∑ i in s, g' i • v i) = 0 := by
-    apply_fun (· • ·) (a : R) at hg
+    apply_fun ((a : R) • ·) at hg
     rw [smul_zero, Finset.smul_sum] at hg
     rw [map_sum, ← hg]
     refine' Finset.sum_congr rfl fun i hi => _

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

This has nice performance benefits.

@@ -31,7 +31,7 @@ open nonZeroDivisors
 
 section Localization
 
-variable {R : Type _} (Rₛ : Type _) [CommRing R] [CommRing Rₛ] [Algebra R Rₛ]
+variable {R : Type*} (Rₛ : Type*) [CommRing R] [CommRing Rₛ] [Algebra R Rₛ]
 
 variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
 
@@ -39,9 +39,9 @@ variable (S : Submonoid R) [hT : IsLocalization S Rₛ]
 
 section AddCommMonoid
 
-variable {M : Type _} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
+variable {M : Type*} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTower R Rₛ M]
 
-theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : LinearIndependent R b) :
+theorem LinearIndependent.localization {ι : Type*} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
   rw [linearIndependent_iff'] at hli ⊢
   intro s g hg i hi
@@ -58,9 +58,9 @@ end AddCommMonoid
 
 section LocalizationLocalization
 
-variable {A : Type _} [CommRing A] [Algebra R A]
+variable {A : Type*} [CommRing A] [Algebra R A]
 
-variable (Aₛ : Type _) [CommRing Aₛ] [Algebra A Aₛ]
+variable (Aₛ : Type*) [CommRing Aₛ] [Algebra A Aₛ]
 
 variable [Algebra Rₛ Aₛ] [Algebra R Aₛ] [IsScalarTower R Rₛ Aₛ] [IsScalarTower R A Aₛ]
 
@@ -70,7 +70,7 @@ variable [hA : IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ]
 
 open Submodule
 
-theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
+theorem LinearIndependent.localization_localization {ι : Type*} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) := by
   rw [linearIndependent_iff'] at hv ⊢
   intro s g hg i hi
@@ -109,19 +109,19 @@ theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
 
 A suitable instance for `[Algebra A Aₛ]` is `localizationAlgebra`.
 -/
-noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A) : Basis ι Rₛ Aₛ :=
+noncomputable def Basis.localizationLocalization {ι : Type*} (b : Basis ι R A) : Basis ι Rₛ Aₛ :=
   Basis.mk (b.linearIndependent.localization_localization _ S _)
     (by rw [Set.range_comp, SpanEqTop.localization_localization Rₛ S Aₛ b.span_eq])
 #align basis.localization_localization Basis.localizationLocalization
 
 @[simp]
-theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
+theorem Basis.localizationLocalization_apply {ι : Type*} (b : Basis ι R A) (i) :
     b.localizationLocalization Rₛ S Aₛ i = algebraMap A Aₛ (b i) :=
   Basis.mk_apply _ _ _
 #align basis.localization_localization_apply Basis.localizationLocalization_apply
 
 @[simp]
-theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :
+theorem Basis.localizationLocalization_repr_algebraMap {ι : Type*} (b : Basis ι R A) (x i) :
     (b.localizationLocalization Rₛ S Aₛ).repr (algebraMap A Aₛ x) i =
       algebraMap R Rₛ (b.repr x i) :=
   calc
@@ -140,7 +140,7 @@ theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis
     _ = algebraMap R Rₛ (b.repr x i) := by simp [Algebra.smul_def]
 #align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMap
 
-theorem Basis.localizationLocalization_span {ι : Type _} (b : Basis ι R A) :
+theorem Basis.localizationLocalization_span {ι : Type*} (b : Basis ι R A) :
     Submodule.span R (Set.range (b.localizationLocalization Rₛ S Aₛ)) =
       LinearMap.range (IsScalarTower.toAlgHom R A Aₛ) :=
   calc span R (Set.range ↑(localizationLocalization Rₛ S Aₛ b))
@@ -154,11 +154,11 @@ end Localization
 
 section FractionRing
 
-variable (R K : Type _) [CommRing R] [Field K] [Algebra R K] [IsFractionRing R K]
+variable (R K : Type*) [CommRing R] [Field K] [Algebra R K] [IsFractionRing R K]
 
-variable {V : Type _} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
+variable {V : Type*} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
 
-theorem LinearIndependent.iff_fractionRing {ι : Type _} {b : ι → V} :
+theorem LinearIndependent.iff_fractionRing {ι : Type*} {b : ι → V} :
     LinearIndependent R b ↔ LinearIndependent K b :=
   ⟨LinearIndependent.localization K R⁰,
     LinearIndependent.restrict_scalars (smul_left_injective R one_ne_zero)⟩
@@ -168,9 +168,9 @@ end FractionRing
 
 section
 
-variable {R : Type _} [CommRing R] (S : Submonoid R)
-variable (A : Type _) [CommRing A] [Algebra R A] [IsLocalization S A]
-variable {M N : Type _}
+variable {R : Type*} [CommRing R] (S : Submonoid R)
+variable (A : Type*) [CommRing A] [Algebra R A] [IsLocalization S A]
+variable {M N : Type*}
   [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
   [AddCommMonoid N] [Module R N] [Module A N] [IsScalarTower R A N]
 

Add the following result:

theorem mem_span_integralBasis {x : K} :
    x ∈ Submodule.span ℤ (Set.range (integralBasis K)) ↔ x ∈ 𝓞 K

that is, integralBasis is indeed a ℤ-basis of the ring of integers.

Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com>

Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com>

@@ -140,6 +140,14 @@ theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis
     _ = algebraMap R Rₛ (b.repr x i) := by simp [Algebra.smul_def]
 #align basis.localization_localization_repr_algebra_map Basis.localizationLocalization_repr_algebraMap
 
+theorem Basis.localizationLocalization_span {ι : Type _} (b : Basis ι R A) :
+    Submodule.span R (Set.range (b.localizationLocalization Rₛ S Aₛ)) =
+      LinearMap.range (IsScalarTower.toAlgHom R A Aₛ) :=
+  calc span R (Set.range ↑(localizationLocalization Rₛ S Aₛ b))
+    _ = span R (↑(IsScalarTower.toAlgHom R A Aₛ) '' Set.range ↑b) := by congr; ext; simp
+    _ = map (IsScalarTower.toAlgHom R A Aₛ) (span R (Set.range b)) := by rw [Submodule.map_span]
+    _ = LinearMap.range (IsScalarTower.toAlgHom R A Aₛ) := by rw [b.span_eq, Submodule.map_top]
+
 end LocalizationLocalization
 
 end Localization

Port of leanprover-community/mathlib#17973

Follow up work:

• add IsPushout when M is a CommRing.

Co-authored-by: Calvin Lee <calvins.lee@utah.edu> Co-authored-by: Calvin Lee <pounce@integraldoma.in>

@@ -157,3 +157,37 @@ theorem LinearIndependent.iff_fractionRing {ι : Type _} {b : ι → V} :
 #align linear_independent.iff_fraction_ring LinearIndependent.iff_fractionRing
 
 end FractionRing
+
+section
+
+variable {R : Type _} [CommRing R] (S : Submonoid R)
+variable (A : Type _) [CommRing A] [Algebra R A] [IsLocalization S A]
+variable {M N : Type _}
+  [AddCommMonoid M] [Module R M] [Module A M] [IsScalarTower R A M]
+  [AddCommMonoid N] [Module R N] [Module A N] [IsScalarTower R A N]
+
+open IsLocalization
+
+/-- An `R`-linear map between two `S⁻¹R`-modules is actually `S⁻¹R`-linear. -/
+def LinearMap.extendScalarsOfIsLocalization (f : M →ₗ[R] N) : M →ₗ[A] N where
+  toFun := f
+  map_add' := f.map_add
+  map_smul' := by
+    intro r m
+    simp only [RingHom.id_apply]
+    rcases mk'_surjective S r with ⟨r, s, rfl⟩
+    calc f (mk' A r s • m)
+        = ((s : R) • mk' A 1 s) • f (mk' A r s • m) := by simp
+      _ = (mk' A 1 s) • (s : R) • f (mk' A r s • m) := by rw [smul_comm, smul_assoc]
+      _ = (mk' A 1 s) • f ((s : R) • mk' A r s • m) := by simp
+      _ = (mk' A 1 s) • f (r • m) := by rw [← smul_assoc, smul_mk'_self, algebraMap_smul]
+      _ = (mk' A 1 s) • r • f m := by simp
+      _ = mk' A r s • f m := by rw [smul_comm, ← smul_assoc, smul_mk'_one]
+
+@[simp] lemma LinearMap.restrictScalars_extendScalarsOfIsLocalization (f : M →ₗ[R] N) :
+    (f.extendScalarsOfIsLocalization S A).restrictScalars R = f := rfl
+
+@[simp] lemma LinearMap.extendScalarsOfIsLocalization_apply (f : M →ₗ[A] N) :
+    f.extendScalarsOfIsLocalization S A = f := rfl
+
+end

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Junyan Xu, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.module
-! leanprover-community/mathlib commit 2e59a6de168f95d16b16d217b808a36290398c0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Basis
 import Mathlib.RingTheory.Localization.FractionRing
 import Mathlib.RingTheory.Localization.Integer
 
+#align_import ring_theory.localization.module from "leanprover-community/mathlib"@"2e59a6de168f95d16b16d217b808a36290398c0a"
+
 /-!
 # Modules / vector spaces over localizations / fraction fields
 

Changes are of the form

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

@@ -46,7 +46,7 @@ variable {M : Type _} [AddCommMonoid M] [Module R M] [Module Rₛ M] [IsScalarTo
 
 theorem LinearIndependent.localization {ι : Type _} {b : ι → M} (hli : LinearIndependent R b) :
     LinearIndependent Rₛ b := by
-  rw [linearIndependent_iff'] at hli⊢
+  rw [linearIndependent_iff'] at hli ⊢
   intro s g hg i hi
   choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
   specialize hli s g' _ i hi
@@ -75,11 +75,11 @@ open Submodule
 
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) := by
-  rw [linearIndependent_iff'] at hv⊢
+  rw [linearIndependent_iff'] at hv ⊢
   intro s g hg i hi
   choose! a g' hg' using IsLocalization.exist_integer_multiples S s g
   have h0 : algebraMap A Aₛ (∑ i in s, g' i • v i) = 0 := by
-    apply_fun (· • ·) (a : R)  at hg
+    apply_fun (· • ·) (a : R) at hg
     rw [smul_zero, Finset.smul_sum] at hg
     rw [map_sum, ← hg]
     refine' Finset.sum_congr rfl fun i hi => _

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -73,7 +73,6 @@ variable [hA : IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ]
 
 open Submodule
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
     (hv : LinearIndependent R v) : LinearIndependent Rₛ (algebraMap A Aₛ ∘ v) := by
   rw [linearIndependent_iff'] at hv⊢
@@ -94,7 +93,6 @@ theorem LinearIndependent.localization_localization {ι : Type _} {v : ι → A}
   exact (IsLocalization.map_eq_zero_iff S _ _).2 ⟨⟨r, hrS⟩, hv⟩
 #align linear_independent.localization_localization LinearIndependent.localization_localization
 
-set_option synthInstance.etaExperiment true in
 theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
     span Rₛ (algebraMap A Aₛ '' v) = ⊤ := by
   rw [eq_top_iff]
@@ -110,7 +108,6 @@ theorem SpanEqTop.localization_localization {v : Set A} (hv : span R v = ⊤) :
   exact mem_map_of_mem (hv.symm ▸ mem_top)
 #align span_eq_top.localization_localization SpanEqTop.localization_localization
 
-set_option synthInstance.etaExperiment true in
 /-- If `A` has an `R`-basis, then localizing `A` at `S` has a basis over `R` localized at `S`.
 
 A suitable instance for `[Algebra A Aₛ]` is `localizationAlgebra`.
@@ -120,14 +117,12 @@ noncomputable def Basis.localizationLocalization {ι : Type _} (b : Basis ι R A
     (by rw [Set.range_comp, SpanEqTop.localization_localization Rₛ S Aₛ b.span_eq])
 #align basis.localization_localization Basis.localizationLocalization
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem Basis.localizationLocalization_apply {ι : Type _} (b : Basis ι R A) (i) :
     b.localizationLocalization Rₛ S Aₛ i = algebraMap A Aₛ (b i) :=
   Basis.mk_apply _ _ _
 #align basis.localization_localization_apply Basis.localizationLocalization_apply
 
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem Basis.localizationLocalization_repr_algebraMap {ι : Type _} (b : Basis ι R A) (x i) :
     (b.localizationLocalization Rₛ S Aₛ).repr (algebraMap A Aₛ x) i =
@@ -158,7 +153,6 @@ variable (R K : Type _) [CommRing R] [Field K] [Algebra R K] [IsFractionRing R K
 
 variable {V : Type _} [AddCommGroup V] [Module R V] [Module K V] [IsScalarTower R K V]
 
-set_option synthInstance.etaExperiment true in
 theorem LinearIndependent.iff_fractionRing {ι : Type _} {b : ι → V} :
     LinearIndependent R b ↔ LinearIndependent K b :=
   ⟨LinearIndependent.localization K R⁰,