linear_algebra.std_basis ⟷ Mathlib.LinearAlgebra.StdBasis

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

@@ -140,7 +140,7 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
   SetLike.le_def.2
     (by
       intro b hb
-      simp only [mem_infi, mem_ker, proj_apply] at hb 
+      simp only [mem_infi, mem_ker, proj_apply] at hb
       rw [←
         show ∑ i in I, std_basis R φ i (b i) = b by
           ext i

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

@@ -190,6 +190,11 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     funext_iff]
   rintro b ⟨hI, hJ⟩ i
   classical
+  by_cases hiI : i ∈ I
+  · by_cases hiJ : i ∈ J
+    · exact (h.le_bot ⟨hiI, hiJ⟩).elim
+    · exact hJ i hiJ
+  · exact hI i hiI
 #align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasis
 -/
 

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

@@ -190,11 +190,6 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     funext_iff]
   rintro b ⟨hI, hJ⟩ i
   classical
-  by_cases hiI : i ∈ I
-  · by_cases hiJ : i ∈ J
-    · exact (h.le_bot ⟨hiI, hiJ⟩).elim
-    · exact hJ i hiJ
-  · exact hI i hiI
 #align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasis
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.Data.Matrix.Basis
-import Mathbin.LinearAlgebra.Basis
-import Mathbin.LinearAlgebra.Pi
+import Data.Matrix.Basis
+import LinearAlgebra.Basis
+import LinearAlgebra.Pi
 
 #align_import linear_algebra.std_basis from "leanprover-community/mathlib"@"13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module linear_algebra.std_basis
-! leanprover-community/mathlib commit 13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Matrix.Basis
 import Mathbin.LinearAlgebra.Basis
 import Mathbin.LinearAlgebra.Pi
 
+#align_import linear_algebra.std_basis from "leanprover-community/mathlib"@"13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395"
+
 /-!
 # The standard basis
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -94,7 +94,7 @@ theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j =
 #print LinearMap.stdBasis_eq_pi_diag /-
 theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   by
-  ext (x j)
+  ext x j
   convert (update_apply 0 x i j _).symm
   rfl
 #align linear_map.std_basis_eq_pi_diag LinearMap.stdBasis_eq_pi_diag
@@ -377,7 +377,7 @@ variable {n m}
 theorem stdBasis_eq_stdBasisMatrix (i : n) (j : m) [DecidableEq n] [DecidableEq m] :
     stdBasis R n m (i, j) = stdBasisMatrix i j (1 : R) :=
   by
-  ext (a b)
+  ext a b
   by_cases hi : i = a <;> by_cases hj : j = b
   · simp [std_basis, hi, hj]
   · simp [std_basis, hi, hj, Ne.symm hj, LinearMap.stdBasis_ne]

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

@@ -57,53 +57,74 @@ def stdBasis : ∀ i : ι, φ i →ₗ[R] ∀ i, φ i :=
 #align linear_map.std_basis LinearMap.stdBasis
 -/
 
+#print LinearMap.stdBasis_apply /-
 theorem stdBasis_apply (i : ι) (b : φ i) : stdBasis R φ i b = update 0 i b :=
   rfl
 #align linear_map.std_basis_apply LinearMap.stdBasis_apply
+-/
 
+#print LinearMap.stdBasis_apply' /-
 @[simp]
 theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = ite (i = i') 1 0 :=
   by
   rw [LinearMap.stdBasis_apply, Function.update_apply, Pi.zero_apply]
   congr 1; rw [eq_iff_iff, eq_comm]
 #align linear_map.std_basis_apply' LinearMap.stdBasis_apply'
+-/
 
+#print LinearMap.coe_stdBasis /-
 theorem coe_stdBasis (i : ι) : ⇑(stdBasis R φ i) = Pi.single i :=
   rfl
 #align linear_map.coe_std_basis LinearMap.coe_stdBasis
+-/
 
+#print LinearMap.stdBasis_same /-
 @[simp]
 theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
   Pi.single_eq_same i b
 #align linear_map.std_basis_same LinearMap.stdBasis_same
+-/
 
+#print LinearMap.stdBasis_ne /-
 theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j = 0 :=
   Pi.single_eq_of_ne h b
 #align linear_map.std_basis_ne LinearMap.stdBasis_ne
+-/
 
+#print LinearMap.stdBasis_eq_pi_diag /-
 theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   by
   ext (x j)
   convert (update_apply 0 x i j _).symm
   rfl
 #align linear_map.std_basis_eq_pi_diag LinearMap.stdBasis_eq_pi_diag
+-/
 
+#print LinearMap.ker_stdBasis /-
 theorem ker_stdBasis (i : ι) : ker (stdBasis R φ i) = ⊥ :=
   ker_eq_bot_of_injective <| Pi.single_injective _ _
 #align linear_map.ker_std_basis LinearMap.ker_stdBasis
+-/
 
+#print LinearMap.proj_comp_stdBasis /-
 theorem proj_comp_stdBasis (i j : ι) : (proj i).comp (stdBasis R φ j) = diag j i := by
   rw [std_basis_eq_pi_diag, proj_pi]
 #align linear_map.proj_comp_std_basis LinearMap.proj_comp_stdBasis
+-/
 
+#print LinearMap.proj_stdBasis_same /-
 theorem proj_stdBasis_same (i : ι) : (proj i).comp (stdBasis R φ i) = id :=
   LinearMap.ext <| stdBasis_same R φ i
 #align linear_map.proj_std_basis_same LinearMap.proj_stdBasis_same
+-/
 
+#print LinearMap.proj_stdBasis_ne /-
 theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ j) = 0 :=
   LinearMap.ext <| stdBasis_ne R φ _ _ h
 #align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_ne
+-/
 
+#print LinearMap.iSup_range_stdBasis_le_iInf_ker_proj /-
 theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
     (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
   by
@@ -114,7 +135,9 @@ theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
   rintro rfl
   exact h.le_bot ⟨hi, hj⟩
 #align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_proj
+-/
 
+#print LinearMap.iInf_ker_proj_le_iSup_range_stdBasis /-
 theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
     (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
   SetLike.le_def.2
@@ -131,7 +154,9 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
           exact hb _ ((hu trivial).resolve_left hiI)]
       exact sum_mem_bsupr fun i hi => mem_range_self (std_basis R φ i) (b i))
 #align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasis
+-/
 
+#print LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj /-
 theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
     (⨆ i ∈ I, range (stdBasis R φ i)) = ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
@@ -142,7 +167,9 @@ theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
   rw [Set.Finite.mem_toFinset]
   exact le_rfl
 #align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj
+-/
 
+#print LinearMap.iSup_range_stdBasis /-
 theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ :=
   by
   cases nonempty_fintype ι
@@ -153,7 +180,9 @@ theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤
         ((@iSup_pos _ _ _ fun h => range <| std_basis R φ i) <| Finset.mem_univ i).symm
   · rw [Finset.coe_univ, Set.union_empty]
 #align linear_map.supr_range_std_basis LinearMap.iSup_range_stdBasis
+-/
 
+#print LinearMap.disjoint_stdBasis_stdBasis /-
 theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     Disjoint (⨆ i ∈ I, range (stdBasis R φ i)) (⨆ i ∈ J, range (stdBasis R φ i)) :=
   by
@@ -170,11 +199,14 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     · exact hJ i hiJ
   · exact hI i hiI
 #align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasis
+-/
 
+#print LinearMap.stdBasis_eq_single /-
 theorem stdBasis_eq_single {a : R} :
     (fun i : ι => (stdBasis R (fun _ : ι => R) i) a) = fun i : ι => Finsupp.single i a :=
   funext fun i => (Finsupp.single_eq_pi_single i a).symm
 #align linear_map.std_basis_eq_single LinearMap.stdBasis_eq_single
+-/
 
 end LinearMap
 
@@ -190,6 +222,7 @@ section Module
 
 variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
 
+#print Pi.linearIndependent_stdBasis /-
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
     LinearIndependent R fun ji : Σ j, ιs j => stdBasis R Ms ji.1 (v ji.1 ji.2) :=
@@ -221,6 +254,7 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
       convert Set.disjoint_singleton_left.2 hiJ using 0
     exact (disjoint_std_basis_std_basis _ _ _ _ h₃).mono h₁ h₂
 #align pi.linear_independent_std_basis Pi.linearIndependent_stdBasis
+-/
 
 variable [Semiring R] [∀ i, AddCommMonoid (Ms i)] [∀ i, Module R (Ms i)]
 
@@ -246,6 +280,7 @@ protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
 #align pi.basis Pi.basis
 -/
 
+#print Pi.basis_repr_stdBasis /-
 @[simp]
 theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (j i) :
     (Pi.basis s).repr (stdBasis R _ j (s j i)) = Finsupp.single ⟨j, i⟩ 1 :=
@@ -267,18 +302,23 @@ theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j))
   rintro ⟨⟩
   contradiction
 #align pi.basis_repr_std_basis Pi.basis_repr_stdBasis
+-/
 
+#print Pi.basis_apply /-
 @[simp]
 theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
     Pi.basis s ji = stdBasis R _ ji.1 (s ji.1 ji.2) :=
   Basis.apply_eq_iff.mpr (by simp)
 #align pi.basis_apply Pi.basis_apply
+-/
 
+#print Pi.basis_repr /-
 @[simp]
 theorem basis_repr (s : ∀ j, Basis (ιs j) R (Ms j)) (x) (ji) :
     (Pi.basis s).repr x ji = (s ji.1).repr (x ji.1) ji.2 :=
   rfl
 #align pi.basis_repr Pi.basis_repr
+-/
 
 end
 
@@ -293,20 +333,26 @@ noncomputable def basisFun : Basis η R (∀ j : η, R) :=
 #align pi.basis_fun Pi.basisFun
 -/
 
+#print Pi.basisFun_apply /-
 @[simp]
 theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun i : η => R) i 1 := by
   simp only [basis_fun, Basis.coe_ofEquivFun, LinearEquiv.refl_symm, LinearEquiv.refl_apply,
     std_basis_apply]
 #align pi.basis_fun_apply Pi.basisFun_apply
+-/
 
+#print Pi.basisFun_repr /-
 @[simp]
 theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basis_fun]
 #align pi.basis_fun_repr Pi.basisFun_repr
+-/
 
+#print Pi.basisFun_equivFun /-
 @[simp]
 theorem basisFun_equivFun : (Pi.basisFun R η).equivFun = LinearEquiv.refl _ _ :=
   Basis.equivFun_ofEquivFun _
 #align pi.basis_fun_equiv_fun Pi.basisFun_equivFun
+-/
 
 end
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -122,7 +122,7 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
       intro b hb
       simp only [mem_infi, mem_ker, proj_apply] at hb 
       rw [←
-        show (∑ i in I, std_basis R φ i (b i)) = b by
+        show ∑ i in I, std_basis R φ i (b i) = b by
           ext i
           rw [Finset.sum_apply, ← std_basis_same R φ i (b i)]
           refine' Finset.sum_eq_single i (fun j hjI ne => std_basis_ne _ _ _ _ Ne.symm _) _

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

@@ -84,7 +84,7 @@ theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j =
 theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   by
   ext (x j)
-  convert(update_apply 0 x i j _).symm
+  convert (update_apply 0 x i j _).symm
   rfl
 #align linear_map.std_basis_eq_pi_diag LinearMap.stdBasis_eq_pi_diag
 
@@ -164,11 +164,11 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     funext_iff]
   rintro b ⟨hI, hJ⟩ i
   classical
-    by_cases hiI : i ∈ I
-    · by_cases hiJ : i ∈ J
-      · exact (h.le_bot ⟨hiI, hiJ⟩).elim
-      · exact hJ i hiJ
-    · exact hI i hiI
+  by_cases hiI : i ∈ I
+  · by_cases hiJ : i ∈ J
+    · exact (h.le_bot ⟨hiI, hiJ⟩).elim
+    · exact hJ i hiJ
+  · exact hI i hiI
 #align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasis
 
 theorem stdBasis_eq_single {a : R} :

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

@@ -120,7 +120,7 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
   SetLike.le_def.2
     (by
       intro b hb
-      simp only [mem_infi, mem_ker, proj_apply] at hb
+      simp only [mem_infi, mem_ker, proj_apply] at hb 
       rw [←
         show (∑ i in I, std_basis R φ i (b i)) = b by
           ext i
@@ -192,7 +192,7 @@ variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
 
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
-    LinearIndependent R fun ji : Σj, ιs j => stdBasis R Ms ji.1 (v ji.1 ji.2) :=
+    LinearIndependent R fun ji : Σ j, ιs j => stdBasis R Ms ji.1 (v ji.1 ji.2) :=
   by
   have hs' : ∀ j : η, LinearIndependent R fun i : ιs j => std_basis R Ms j (v j i) :=
     by
@@ -237,7 +237,7 @@ given by `s j` on each component.
 For the standard basis over `R` on the finite-dimensional space `η → R` see `pi.basis_fun`.
 -/
 protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
-    Basis (Σj, ιs j) R (∀ j, Ms j) :=
+    Basis (Σ j, ιs j) R (∀ j, Ms j) :=
   by
   -- The `add_comm_monoid (Π j, Ms j)` instance was hard to find.
   -- Defining this in tactic mode seems to shake up instance search enough that it works by itself.
@@ -258,7 +258,7 @@ theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j))
     symm
     exact
       Finsupp.single_apply_left
-        (fun i i' (h : (⟨j, i⟩ : Σj, ιs j) = ⟨j, i'⟩) => eq_of_hEq (Sigma.mk.inj h).2) _ _ _
+        (fun i i' (h : (⟨j, i⟩ : Σ j, ιs j) = ⟨j, i'⟩) => eq_of_hEq (Sigma.mk.inj h).2) _ _ _
   simp only [Pi.basis, LinearEquiv.trans_apply, Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply,
     LinearEquiv.piCongrRight]
   dsimp

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

@@ -43,7 +43,7 @@ this is a basis over `fin 3 → R`.
 
 open Function Submodule
 
-open BigOperators
+open scoped BigOperators
 
 namespace LinearMap
 

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

@@ -57,22 +57,10 @@ def stdBasis : ∀ i : ι, φ i →ₗ[R] ∀ i, φ i :=
 #align linear_map.std_basis LinearMap.stdBasis
 -/
 
-/- warning: linear_map.std_basis_apply -> LinearMap.stdBasis_apply is a dubious translation:
-lean 3 declaration is
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 theorem stdBasis_apply (i : ι) (b : φ i) : stdBasis R φ i b = update 0 i b :=
   rfl
 #align linear_map.std_basis_apply LinearMap.stdBasis_apply
 
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 @[simp]
 theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = ite (i = i') 1 0 :=
   by
@@ -80,40 +68,19 @@ theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = i
   congr 1; rw [eq_iff_iff, eq_comm]
 #align linear_map.std_basis_apply' LinearMap.stdBasis_apply'
 
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 theorem coe_stdBasis (i : ι) : ⇑(stdBasis R φ i) = Pi.single i :=
   rfl
 #align linear_map.coe_std_basis LinearMap.coe_stdBasis
 
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 @[simp]
 theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
   Pi.single_eq_same i b
 #align linear_map.std_basis_same LinearMap.stdBasis_same
 
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 theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j = 0 :=
   Pi.single_eq_of_ne h b
 #align linear_map.std_basis_ne LinearMap.stdBasis_ne
 
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 theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   by
   ext (x j)
@@ -121,40 +88,22 @@ theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   rfl
 #align linear_map.std_basis_eq_pi_diag LinearMap.stdBasis_eq_pi_diag
 
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 theorem ker_stdBasis (i : ι) : ker (stdBasis R φ i) = ⊥ :=
   ker_eq_bot_of_injective <| Pi.single_injective _ _
 #align linear_map.ker_std_basis LinearMap.ker_stdBasis
 
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 theorem proj_comp_stdBasis (i j : ι) : (proj i).comp (stdBasis R φ j) = diag j i := by
   rw [std_basis_eq_pi_diag, proj_pi]
 #align linear_map.proj_comp_std_basis LinearMap.proj_comp_stdBasis
 
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 theorem proj_stdBasis_same (i : ι) : (proj i).comp (stdBasis R φ i) = id :=
   LinearMap.ext <| stdBasis_same R φ i
 #align linear_map.proj_std_basis_same LinearMap.proj_stdBasis_same
 
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 theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ j) = 0 :=
   LinearMap.ext <| stdBasis_ne R φ _ _ h
 #align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_ne
 
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 theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
     (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
   by
@@ -166,9 +115,6 @@ theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
   exact h.le_bot ⟨hi, hj⟩
 #align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_proj
 
-/- warning: linear_map.infi_ker_proj_le_supr_range_std_basis -> LinearMap.iInf_ker_proj_le_iSup_range_stdBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasisₓ'. -/
 theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
     (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
   SetLike.le_def.2
@@ -186,9 +132,6 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
       exact sum_mem_bsupr fun i hi => mem_range_self (std_basis R φ i) (b i))
 #align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasis
 
-/- warning: linear_map.supr_range_std_basis_eq_infi_ker_proj -> LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_projₓ'. -/
 theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
     (⨆ i ∈ I, range (stdBasis R φ i)) = ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
@@ -200,12 +143,6 @@ theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
   exact le_rfl
 #align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj
 
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 theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ :=
   by
   cases nonempty_fintype ι
@@ -217,9 +154,6 @@ theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤
   · rw [Finset.coe_univ, Set.union_empty]
 #align linear_map.supr_range_std_basis LinearMap.iSup_range_stdBasis
 
-/- warning: linear_map.disjoint_std_basis_std_basis -> LinearMap.disjoint_stdBasis_stdBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasisₓ'. -/
 theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     Disjoint (⨆ i ∈ I, range (stdBasis R φ i)) (⨆ i ∈ J, range (stdBasis R φ i)) :=
   by
@@ -237,12 +171,6 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     · exact hI i hiI
 #align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasis
 
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 theorem stdBasis_eq_single {a : R} :
     (fun i : ι => (stdBasis R (fun _ : ι => R) i) a) = fun i : ι => Finsupp.single i a :=
   funext fun i => (Finsupp.single_eq_pi_single i a).symm
@@ -262,9 +190,6 @@ section Module
 
 variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
 
-/- warning: pi.linear_independent_std_basis -> Pi.linearIndependent_stdBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pi.linear_independent_std_basis Pi.linearIndependent_stdBasisₓ'. -/
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
     LinearIndependent R fun ji : Σj, ιs j => stdBasis R Ms ji.1 (v ji.1 ji.2) :=
@@ -321,9 +246,6 @@ protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
 #align pi.basis Pi.basis
 -/
 
-/- warning: pi.basis_repr_std_basis -> Pi.basis_repr_stdBasis is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align pi.basis_repr_std_basis Pi.basis_repr_stdBasisₓ'. -/
 @[simp]
 theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (j i) :
     (Pi.basis s).repr (stdBasis R _ j (s j i)) = Finsupp.single ⟨j, i⟩ 1 :=
@@ -346,18 +268,12 @@ theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j))
   contradiction
 #align pi.basis_repr_std_basis Pi.basis_repr_stdBasis
 
-/- warning: pi.basis_apply -> Pi.basis_apply is a dubious translation:
-<too large>
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 @[simp]
 theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
     Pi.basis s ji = stdBasis R _ ji.1 (s ji.1 ji.2) :=
   Basis.apply_eq_iff.mpr (by simp)
 #align pi.basis_apply Pi.basis_apply
 
-/- warning: pi.basis_repr -> Pi.basis_repr is a dubious translation:
-<too large>
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 @[simp]
 theorem basis_repr (s : ∀ j, Basis (ιs j) R (Ms j)) (x) (ji) :
     (Pi.basis s).repr x ji = (s ji.1).repr (x ji.1) ji.2 :=
@@ -377,28 +293,16 @@ noncomputable def basisFun : Basis η R (∀ j : η, R) :=
 #align pi.basis_fun Pi.basisFun
 -/
 
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 @[simp]
 theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun i : η => R) i 1 := by
   simp only [basis_fun, Basis.coe_ofEquivFun, LinearEquiv.refl_symm, LinearEquiv.refl_apply,
     std_basis_apply]
 #align pi.basis_fun_apply Pi.basisFun_apply
 
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-<too large>
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 @[simp]
 theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basis_fun]
 #align pi.basis_fun_repr Pi.basisFun_repr
 
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 @[simp]
 theorem basisFun_equivFun : (Pi.basisFun R η).equivFun = LinearEquiv.refl _ _ :=
   Basis.equivFun_ofEquivFun _

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

@@ -102,10 +102,7 @@ theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
 #align linear_map.std_basis_same LinearMap.stdBasis_same
 
 /- warning: linear_map.std_basis_ne -> LinearMap.stdBasis_ne is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_ne LinearMap.stdBasis_neₓ'. -/
 theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j = 0 :=
   Pi.single_eq_of_ne h b
@@ -135,40 +132,28 @@ theorem ker_stdBasis (i : ι) : ker (stdBasis R φ i) = ⊥ :=
 #align linear_map.ker_std_basis LinearMap.ker_stdBasis
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.proj_comp_std_basis LinearMap.proj_comp_stdBasisₓ'. -/
 theorem proj_comp_stdBasis (i j : ι) : (proj i).comp (stdBasis R φ j) = diag j i := by
   rw [std_basis_eq_pi_diag, proj_pi]
 #align linear_map.proj_comp_std_basis LinearMap.proj_comp_stdBasis
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.proj_std_basis_same LinearMap.proj_stdBasis_sameₓ'. -/
 theorem proj_stdBasis_same (i : ι) : (proj i).comp (stdBasis R φ i) = id :=
   LinearMap.ext <| stdBasis_same R φ i
 #align linear_map.proj_std_basis_same LinearMap.proj_stdBasis_same
 
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 Case conversion may be inaccurate. Consider using '#align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_neₓ'. -/
 theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ j) = 0 :=
   LinearMap.ext <| stdBasis_ne R φ _ _ h
 #align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_ne
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_projₓ'. -/
 theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
     (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
@@ -182,10 +167,7 @@ theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
 #align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_proj
 
 /- warning: linear_map.infi_ker_proj_le_supr_range_std_basis -> LinearMap.iInf_ker_proj_le_iSup_range_stdBasis is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasisₓ'. -/
 theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
     (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
@@ -205,10 +187,7 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
 #align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasis
 
 /- warning: linear_map.supr_range_std_basis_eq_infi_ker_proj -> LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_projₓ'. -/
 theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
@@ -239,10 +218,7 @@ theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤
 #align linear_map.supr_range_std_basis LinearMap.iSup_range_stdBasis
 
 /- warning: linear_map.disjoint_std_basis_std_basis -> LinearMap.disjoint_stdBasis_stdBasis is a dubious translation:
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i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) 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ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max 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+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasisₓ'. -/
 theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     Disjoint (⨆ i ∈ I, range (stdBasis R φ i)) (⨆ i ∈ J, range (stdBasis R φ i)) :=
@@ -287,10 +263,7 @@ section Module
 variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
 
 /- warning: pi.linear_independent_std_basis -> Pi.linearIndependent_stdBasis is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align pi.linear_independent_std_basis Pi.linearIndependent_stdBasisₓ'. -/
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
@@ -349,10 +322,7 @@ protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
 -/
 
 /- warning: pi.basis_repr_std_basis -> Pi.basis_repr_stdBasis is a dubious translation:
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R _inst_1))) (Finsupp.addCommMonoid.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u4 u1} R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Module.toDistribMulAction.{u2, max (max u2 u4) u3} R (Finsupp.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{max u4 u3, u2, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u4 u1, max (max u2 u4) u3, max (max (max u2 u4) u3) u1} R (forall (j : η), Ms j) (Finsupp.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u4 u1, max u2 u4 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (forall (j : η), Ms j) (Finsupp.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms 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+<too large>
 Case conversion may be inaccurate. Consider using '#align pi.basis_repr_std_basis Pi.basis_repr_stdBasisₓ'. -/
 @[simp]
 theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (j i) :
@@ -377,10 +347,7 @@ theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j))
 #align pi.basis_repr_std_basis Pi.basis_repr_stdBasis
 
 /- warning: pi.basis_apply -> Pi.basis_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align pi.basis_apply Pi.basis_applyₓ'. -/
 @[simp]
 theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
@@ -389,10 +356,7 @@ theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
 #align pi.basis_apply Pi.basis_apply
 
 /- warning: pi.basis_repr -> Pi.basis_repr is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align pi.basis_repr Pi.basis_reprₓ'. -/
 @[simp]
 theorem basis_repr (s : ∀ j, Basis (ιs j) R (Ms j)) (x) (ji) :
@@ -414,10 +378,7 @@ noncomputable def basisFun : Basis η R (∀ j : η, R) :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align pi.basis_fun_apply Pi.basisFun_applyₓ'. -/
 @[simp]
 theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun i : η => R) i 1 := by
@@ -426,10 +387,7 @@ theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun
 #align pi.basis_fun_apply Pi.basisFun_apply
 
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_inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1))) (Module.toDistribMulAction.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)))))) (Basis.repr.{u1, u2, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Pi.basisFun.{u2, u1} R η _inst_1 _inst_4)) x) i) (x i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align pi.basis_fun_repr Pi.basisFun_reprₓ'. -/
 @[simp]
 theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basis_fun]

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

@@ -61,7 +61,7 @@ def stdBasis : ∀ i : ι, φ i →ₗ[R] ∀ i, φ i :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{max (succ u2) (succ u3)} (forall (i : ι), φ i) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b) (Function.update.{succ u2, succ u3} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (OfNat.ofNat.{max u2 u3} (forall (a : ι), φ a) 0 (OfNat.mk.{max u2 u3} (forall (a : ι), φ a) 0 (Zero.zero.{max u2 u3} (forall (a : ι), φ a) (Pi.instZero.{u2, u3} ι (fun (a : ι) => φ a) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (φ i) (AddMonoid.toAddZeroClass.{u3} (φ i) (AddCommMonoid.toAddMonoid.{u3} (φ i) (_inst_2 i)))))))) i b)
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (b : φ i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b) (Function.update.{succ u3, succ u2} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (OfNat.ofNat.{max u3 u2} (forall (a : ι), φ a) 0 (Zero.toOfNat0.{max u3 u2} (forall (a : ι), φ a) (Pi.instZero.{u3, u2} ι (fun (a : ι) => φ a) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i)))))) i b)
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (b : φ i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : φ i) => forall (i : ι), φ i) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b) (Function.update.{succ u3, succ u2} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (OfNat.ofNat.{max u3 u2} (forall (a : ι), φ a) 0 (Zero.toOfNat0.{max u3 u2} (forall (a : ι), φ a) (Pi.instZero.{u3, u2} ι (fun (a : ι) => φ a) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i)))))) i b)
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_apply LinearMap.stdBasis_applyₓ'. -/
 theorem stdBasis_apply (i : ι) (b : φ i) : stdBasis R φ i b = update 0 i b :=
   rfl
@@ -71,7 +71,7 @@ theorem stdBasis_apply (i : ι) (b : φ i) : stdBasis R φ i b = update 0 i b :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (i' : ι), Eq.{succ u1} ((fun (_x : ι) => R) i') (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i))) => R -> (forall (i : ι), (fun (_x : ι) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) (OfNat.ofNat.{u1} ((fun (_x : ι) => R) i) 1 (OfNat.mk.{u1} ((fun (_x : ι) => R) i) 1 (One.one.{u1} ((fun (_x : ι) => R) i) (AddMonoidWithOne.toOne.{u1} ((fun (_x : ι) => R) i) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))))))) i') (ite.{succ u1} ((fun (_x : ι) => R) i') (Eq.{succ u2} ι i i') (_inst_4 i i') (OfNat.ofNat.{u1} ((fun (_x : ι) => R) i') 1 (OfNat.mk.{u1} ((fun (_x : ι) => R) i') 1 (One.one.{u1} ((fun (_x : ι) => R) i') (AddMonoidWithOne.toOne.{u1} ((fun (_x : ι) => R) i') (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (_x : ι) => R) i') (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (_x : ι) => R) i') (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i') _inst_1))))))) (OfNat.ofNat.{u1} ((fun (_x : ι) => R) i') 0 (OfNat.mk.{u1} ((fun (_x : ι) => R) i') 0 (Zero.zero.{u1} ((fun (_x : ι) => R) i') (MulZeroClass.toHasZero.{u1} ((fun (_x : ι) => R) i') (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} ((fun (_x : ι) => R) i') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i') (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i') _inst_1))))))))
 but is expected to have type
-  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] (i : ι) (i' : ι), Eq.{succ u2} R (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) i') (ite.{succ u2} R (Eq.{succ u1} ι i i') (_inst_4 i i') (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))
+  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] (i : ι) (i' : ι), Eq.{succ u2} R (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) i') (ite.{succ u2} R (Eq.{succ u1} ι i i') (_inst_4 i i') (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_apply' LinearMap.stdBasis_apply'ₓ'. -/
 @[simp]
 theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = ite (i = i') 1 0 :=
@@ -84,7 +84,7 @@ theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = i
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u3) (succ (max u2 u3))} ((φ i) -> (forall (i : ι), φ i)) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Pi.single.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (φ i) (AddMonoid.toAddZeroClass.{u3} (φ i) (AddCommMonoid.toAddMonoid.{u3} (φ i) (_inst_2 i)))) i)
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : φ i), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Pi.single.{u3, u2} ι φ (fun (a : ι) (b : ι) => _inst_4 a b) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i))) i)
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : φ i), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : φ i) => forall (i : ι), φ i) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Pi.single.{u3, u2} ι φ (fun (a : ι) (b : ι) => _inst_4 a b) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i))) i)
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_std_basis LinearMap.coe_stdBasisₓ'. -/
 theorem coe_stdBasis (i : ι) : ⇑(stdBasis R φ i) = Pi.single i :=
   rfl
@@ -94,7 +94,7 @@ theorem coe_stdBasis (i : ι) : ⇑(stdBasis R φ i) = Pi.single i :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{succ u3} (φ i) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b i) b
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{succ u3} (φ i) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b i) b
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{succ u3} (φ i) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b i) b
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_same LinearMap.stdBasis_sameₓ'. -/
 @[simp]
 theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
@@ -105,7 +105,7 @@ theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (j : ι), (Ne.{succ u2} ι j i) -> (forall (b : φ i), Eq.{succ u3} (φ j) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b j) (OfNat.ofNat.{u3} (φ j) 0 (OfNat.mk.{u3} (φ j) 0 (Zero.zero.{u3} (φ j) (AddZeroClass.toHasZero.{u3} (φ j) (AddMonoid.toAddZeroClass.{u3} (φ j) (AddCommMonoid.toAddMonoid.{u3} (φ j) (_inst_2 j))))))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (j : ι), (Ne.{succ u3} ι j i) -> (forall (b : φ i), Eq.{succ u2} (φ j) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b j) (OfNat.ofNat.{u2} (φ j) 0 (Zero.toOfNat0.{u2} (φ j) (AddMonoid.toZero.{u2} (φ j) (AddCommMonoid.toAddMonoid.{u2} (φ j) (_inst_2 j))))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (j : ι), (Ne.{succ u3} ι j i) -> (forall (b : φ i), Eq.{succ u2} (φ j) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b j) (OfNat.ofNat.{u2} (φ j) 0 (Zero.toOfNat0.{u2} (φ j) (AddMonoid.toZero.{u2} (φ j) (AddCommMonoid.toAddMonoid.{u2} (φ j) (_inst_2 j))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_ne LinearMap.stdBasis_neₓ'. -/
 theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j = 0 :=
   Pi.single_eq_of_ne h b
@@ -265,7 +265,7 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_4 : DecidableEq.{succ u2} ι] {a : R}, Eq.{max (succ u2) (succ u1)} (ι -> (forall (i : ι), (fun (_x : ι) => R) i)) (fun (i : ι) => coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i))) => R -> (forall (i : ι), (fun (_x : ι) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) a) (fun (i : ι) => coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Finsupp.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) => ι -> R) (Finsupp.coeFun.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.single.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) i a))
 but is expected to have type
-  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] {a : R}, Eq.{max (succ u2) (succ u1)} (ι -> ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => ι -> R) a)) (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) a) (fun (i : ι) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.single.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) i a))
+  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] {a : R}, Eq.{max (succ u2) (succ u1)} (ι -> ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => ι -> R) a)) (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) a) (fun (i : ι) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.single.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) i a))
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_eq_single LinearMap.stdBasis_eq_singleₓ'. -/
 theorem stdBasis_eq_single {a : R} :
     (fun i : ι => (stdBasis R (fun _ : ι => R) i) a) = fun i : ι => Finsupp.single i a :=
@@ -290,7 +290,7 @@ variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} {η : Type.{u2}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u4}} [_inst_1 : Ring.{u1} R] [_inst_2 : forall (i : η), AddCommGroup.{u4} (Ms i)] [_inst_3 : forall (i : η), Module.{u1, u4} R (Ms i) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i))] [_inst_4 : DecidableEq.{succ u2} η] (v : forall (j : η), (ιs j) -> (Ms j)), (forall (i : η), LinearIndependent.{u3, u1, u4} (ιs i) R (Ms i) (v i) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (_inst_3 i)) -> (LinearIndependent.{max u2 u3, u1, max u2 u4} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (forall (i : η), Ms i) (fun (ji : Sigma.{u2, u3} η (fun (j : η) => ιs j)) => coeFn.{max (succ u4) (succ (max u2 u4)), max (succ u4) (succ (max u2 u4))} (LinearMap.{u1, u1, u4, max u2 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) ((fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i)) ((fun (i : η) => _inst_3 i) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i) (fun (i : η) => (fun (i : η) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u4, max u2 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) ((fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i)) ((fun (i : η) => _inst_3 i) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i) (fun (i : η) => (fun (i : η) => _inst_3 i) i))) => (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) -> (forall (i : η), Ms i)) (LinearMap.hasCoeToFun.{u1, u1, u4, max u2 u4} R R (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) ((fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i)) ((fun (i : η) => _inst_3 i) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i) (fun (i : η) => (fun (i : η) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.stdBasis.{u1, u2, u4} R η (Ring.toSemiring.{u1} R _inst_1) Ms (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i) (fun (a : η) (b : η) => _inst_4 a b) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (v (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u2, u3} η (fun (j : η) => ιs j) ji))) (Ring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i))) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)))
 but is expected to have type
-  forall {R : Type.{u4}} {η : Type.{u2}} {ιs : η -> Type.{u1}} {Ms : η -> Type.{u3}} [_inst_1 : Ring.{u4} R] [_inst_2 : forall (i : η), AddCommGroup.{u3} (Ms i)] [_inst_3 : forall (i : η), Module.{u4, u3} R (Ms i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))] [_inst_4 : DecidableEq.{succ u2} η] (v : forall (j : η), (ιs j) -> (Ms j)), (forall (i : η), LinearIndependent.{u1, u4, u3} (ιs i) R (Ms i) (v i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (_inst_3 i)) -> (LinearIndependent.{max u2 u1, u4, max u2 u3} (Sigma.{u2, u1} η (fun (j : η) => ιs j)) R (forall (i : η), Ms i) (fun (ji : Sigma.{u2, u1} η (fun (j : η) => ιs j)) => FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u4, u4, u3, max u2 u3} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u2 u3} R R (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.stdBasis.{u4, u2, u3} R η (Ring.toSemiring.{u4} R _inst_1) Ms (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i) (fun (a : η) (b : η) => _inst_4 a b) (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (v (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u2, u1} η (fun (j : η) => ιs j) ji))) (Ring.toSemiring.{u4} R _inst_1) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)))
+  forall {R : Type.{u4}} {η : Type.{u2}} {ιs : η -> Type.{u1}} {Ms : η -> Type.{u3}} [_inst_1 : Ring.{u4} R] [_inst_2 : forall (i : η), AddCommGroup.{u3} (Ms i)] [_inst_3 : forall (i : η), Module.{u4, u3} R (Ms i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))] [_inst_4 : DecidableEq.{succ u2} η] (v : forall (j : η), (ιs j) -> (Ms j)), (forall (i : η), LinearIndependent.{u1, u4, u3} (ιs i) R (Ms i) (v i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (_inst_3 i)) -> (LinearIndependent.{max u2 u1, u4, max u2 u3} (Sigma.{u2, u1} η (fun (j : η) => ιs j)) R (forall (i : η), Ms i) (fun (ji : Sigma.{u2, u1} η (fun (j : η) => ιs j)) => FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u4, u4, u3, max u2 u3} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u2 u3} R R (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.stdBasis.{u4, u2, u3} R η (Ring.toSemiring.{u4} R _inst_1) Ms (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i) (fun (a : η) (b : η) => _inst_4 a b) (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (v (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u2, u1} η (fun (j : η) => ιs j) ji))) (Ring.toSemiring.{u4} R _inst_1) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)))
 Case conversion may be inaccurate. Consider using '#align pi.linear_independent_std_basis Pi.linearIndependent_stdBasisₓ'. -/
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
@@ -352,7 +352,7 @@ protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {η : Type.{u2}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : η), AddCommMonoid.{u4} (Ms i)] [_inst_3 : forall (i : η), Module.{u1, u4} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (s : forall (j : η), Basis.{u3, u1, u4} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (j : η) (i : ιs j), Eq.{max (succ (max u2 u3)) (succ u1)} (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ (max u2 u4)) (succ (max (max u2 u3) u1)), max (succ (max u2 u4)) (succ (max (max u2 u3) u1))} (LinearEquiv.{u1, u1, max u2 u4, max (max u2 u3) u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u4, max (max u2 u3) u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => (forall (j : η), Ms j) -> (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u4, max (max u2 u3) u1} R R (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Basis.repr.{max u2 u3, u1, max 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 but is expected to have type
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j) (forall (i : η), Ms i) _inst_1 _inst_1 (_inst_2 j) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 j) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u4, u1} R η _inst_1 Ms (fun (i : η) => _inst_2 i) (fun (j : η) => _inst_3 j) (fun (a : η) (b : η) => _inst_5 a b) j) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ιs j) (fun (_x : ιs j) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ιs j) => Ms j) _x) (Basis.funLike.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (s j) i))) (Finsupp.single.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (Sigma.mk.{u4, u3} η (fun (j : η) => ιs j) j i) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align pi.basis_repr_std_basis Pi.basis_repr_stdBasisₓ'. -/
 @[simp]
 theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (j i) :
@@ -380,7 +380,7 @@ theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j))
 lean 3 declaration is
   forall {R : Type.{u1}} {η : Type.{u2}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : η), AddCommMonoid.{u4} (Ms i)] [_inst_3 : forall (i : η), Module.{u1, u4} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (s : forall (j : η), Basis.{u3, u1, u4} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ji : Sigma.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j)), Eq.{max (succ u2) (succ u4)} (forall (j : η), (fun (j : η) => Ms j) j) (coeFn.{max (succ (max u2 u3)) (succ u1) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (Basis.{max u2 u3, u1, max u2 u4} (Sigma.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j)) R (forall (j : η), (fun (j : η) => Ms j) j) _inst_1 (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => (fun (j : η) => Ms j) j) (fun (i : η) => (fun (j : η) => _inst_2 j) i)) (Pi.module.{u2, u4, u1} η (fun (j : η) => (fun (j : η) => Ms j) j) R _inst_1 (fun (i : η) => (fun (j : 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: η) => (fun (j : η) => ιs j) j) ji)) (coeFn.{max (succ u3) (succ u1) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u1, u4} (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) R (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) (_inst_3 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji))) (fun (_x : Basis.{u3, u1, u4} (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) R (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) (_inst_3 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji))) => (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) -> (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji))) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u4), succ u3, succ u4} 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=> (fun (j : η) => ιs j) j) ji)))
 but is expected to have type
-  forall {R : Type.{u2}} {η : Type.{u4}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : η), AddCommMonoid.{u1} (Ms i)] [_inst_3 : forall (i : η), Module.{u2, u1} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u4} η] [_inst_5 : DecidableEq.{succ u4} η] (s : forall (j : η), Basis.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)), Eq.{max (succ u4) (succ u1)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) ji) (FunLike.coe.{max (max (max (succ u2) (succ u4)) (succ u3)) (succ u1), max (succ u4) (succ u3), max (succ u4) (succ u1)} (Basis.{max u3 u4, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Sigma.{u4, u3} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) _x) (Basis.funLike.{max u4 u3, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Pi.basis.{u2, u4, u3, u1} R η (fun (j : η) => ιs j) (fun (j : η) => Ms j) _inst_1 (fun (j : η) => _inst_2 j) (fun (j : η) => _inst_3 j) _inst_4 s) ji) (FunLike.coe.{max (succ u4) (succ u1), succ u1, max (succ u4) (succ u1)} (LinearMap.{u2, u2, u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u4 u1} R R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u4, u1} R η _inst_1 Ms (fun (i : η) => _inst_2 i) (fun (j : η) => _inst_3 j) (fun (a : η) (b : η) => _inst_5 a b) (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (fun (_x : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _x) (Basis.funLike.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (s (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)))
+  forall {R : Type.{u2}} {η : Type.{u4}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : η), AddCommMonoid.{u1} (Ms i)] [_inst_3 : forall (i : η), Module.{u2, u1} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u4} η] [_inst_5 : DecidableEq.{succ u4} η] (s : forall (j : η), Basis.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)), Eq.{max (succ u4) (succ u1)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) ji) (FunLike.coe.{max (max (max (succ u2) (succ u4)) (succ u3)) (succ u1), max (succ u4) (succ u3), max (succ u4) (succ u1)} (Basis.{max u3 u4, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Sigma.{u4, u3} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) _x) (Basis.funLike.{max u4 u3, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Pi.basis.{u2, u4, u3, u1} R η (fun (j : η) => ιs j) (fun (j : η) => Ms j) _inst_1 (fun (j : η) => _inst_2 j) (fun (j : η) => _inst_3 j) _inst_4 s) ji) (FunLike.coe.{max (succ u4) (succ u1), succ u1, max (succ u4) (succ u1)} (LinearMap.{u2, u2, u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u4 u1} R R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u4, u1} R η _inst_1 Ms (fun (i : η) => _inst_2 i) (fun (j : η) => _inst_3 j) (fun (a : η) (b : η) => _inst_5 a b) (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (fun (_x : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _x) (Basis.funLike.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (s (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)))
 Case conversion may be inaccurate. Consider using '#align pi.basis_apply Pi.basis_applyₓ'. -/
 @[simp]
 theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
@@ -392,7 +392,7 @@ theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
 lean 3 declaration is
   forall {R : Type.{u1}} {η : Type.{u2}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : η), AddCommMonoid.{u4} (Ms i)] [_inst_3 : forall (i : η), Module.{u1, u4} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u2} η] (s : forall (j : η), Basis.{u3, u1, u4} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (x : forall (j : η), Ms j) (ji : Sigma.{u2, u3} η (fun (j : η) => ιs j)), Eq.{succ u1} R (coeFn.{max (succ (max u2 u3)) (succ u1), max (succ (max u2 u3)) (succ u1)} (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) => (Sigma.{u2, u3} η (fun (j : η) => ιs j)) -> R) (Finsupp.coeFun.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ (max u2 u4)) (succ (max (max u2 u3) u1)), max (succ (max u2 u4)) (succ (max (max u2 u3) u1))} (LinearEquiv.{u1, u1, max u2 u4, max (max u2 u3) u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u4, max (max u2 u3) u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => (forall (j : η), Ms j) -> (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u4, max (max u2 u3) u1} R R (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u3, u1} (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (_inst_3 (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u3, u1, u1} (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Basis.repr.{u3, u1, u4} (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (s (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji))) (x (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji))) (Sigma.snd.{u2, u3} η (fun (j : η) => ιs j) ji))
 but is expected to have type
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(DistribSMul.toSMulZeroClass.{u3, max (max u3 u1) u4} R (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u4} (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u4} (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u3, max (max u3 u1) u4} R (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R 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(MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u3, max u3 u4} R (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u3 u4) u2, u3, u2, max u3 u4} (LinearEquiv.{u3, u3, u2, max u3 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji))) (AddCommMonoid.toAddMonoid.{max u3 u4} (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))))) (Module.toDistribMulAction.{u3, u2} R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji))) (Module.toDistribMulAction.{u3, max u3 u4} R (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u3, u2, max u3 u4, max (max u3 u4) u2} R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (LinearEquiv.{u3, u3, u2, max u3 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, max u3 u4, max (max u3 u4) u2} R R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (LinearEquiv.{u3, u3, u2, max u3 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, max u3 u4} R R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (Basis.repr.{u4, u3, u2} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (s (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji))) (x (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji))) (Sigma.snd.{u1, u4} η (fun (j : η) => ιs j) ji))
+  forall {R : Type.{u3}} {η : Type.{u1}} {ιs : η -> Type.{u4}} {Ms : η -> Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : forall (i : η), AddCommMonoid.{u2} (Ms i)] [_inst_3 : forall (i : η), Module.{u3, u2} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u1} η] (s : forall (j : η), Basis.{u4, u3, u2} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (x : forall (j : η), Ms j) (ji : Sigma.{u1, u4} η (fun (j : η) => ιs j)), Eq.{succ u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u4} η (fun (j : η) => ιs j)) => R) ji) (FunLike.coe.{max (succ (max u1 u4)) (succ u3), succ (max u1 u4), succ u3} (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Sigma.{u1, u4} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u1, u4} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u4} η (fun (j : η) => ιs j)) => R) _x) (Finsupp.funLike.{max u1 u4, u3} (Sigma.{u1, 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(Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u3, u3, u2, max u3 u4, max (max u3 u4) u2} R R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (LinearEquiv.{u3, u3, u2, max u3 u4} R R _inst_1 _inst_1 (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u3, u3, u2, max u3 u4} R R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.addCommMonoid.{u4, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (Finsupp.module.{u4, u3, u3} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)) (RingHomInvPair.ids.{u3} R _inst_1) (RingHomInvPair.ids.{u3} R _inst_1)))))) (Basis.repr.{u4, u3, u2} (ιs (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji)) (s (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji))) (x (Sigma.fst.{u1, u4} η (fun (j : η) => ιs j) ji))) (Sigma.snd.{u1, u4} η (fun (j : η) => ιs j) ji))
 Case conversion may be inaccurate. Consider using '#align pi.basis_repr Pi.basis_reprₓ'. -/
 @[simp]
 theorem basis_repr (s : ∀ j, Basis (ιs j) R (Ms j)) (x) (ji) :
@@ -417,7 +417,7 @@ noncomputable def basisFun : Basis η R (∀ j : η, R) :=
 lean 3 declaration is
   forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (i : η), Eq.{max (succ u2) (succ u1)} (η -> R) (coeFn.{max (succ u2) (succ u1) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (Basis.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : Basis.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => η -> η -> R) (FunLike.hasCoeToFun.{max (succ u2) (succ u1) (succ (max u2 u1)), succ u2, succ (max u2 u1)} (Basis.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) η (fun (_x : η) => η -> R) (Basis.funLike.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))) (Pi.basisFun.{u1, u2} R η _inst_1 _inst_4) i) (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (i : η) => R) i) (forall (i : η), (fun (i : η) => R) i) ((fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => (fun (i : η) => R) i) (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i)) ((fun (i : η) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} η (fun (i : η) => (fun (i : η) => R) i) R _inst_1 (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (fun (i : η) => (fun (i : η) => Semiring.toModule.{u1} R _inst_1) i))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (i : η) => R) i) (forall (i : η), (fun (i : η) => R) i) ((fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => (fun (i : η) => R) i) (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i)) ((fun (i : η) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} η (fun (i : η) => (fun (i : η) => R) i) R _inst_1 (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (fun (i : η) => (fun (i : η) => Semiring.toModule.{u1} R _inst_1) i))) => R -> (forall (i : η), (fun (i : η) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (i : η) => R) i) (forall (i : η), (fun (i : η) => R) i) _inst_1 _inst_1 ((fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => (fun (i : η) => R) i) (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i)) ((fun (i : η) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} η (fun (i : η) => (fun (i : η) => R) i) R _inst_1 (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (fun (i : η) => (fun (i : η) => Semiring.toModule.{u1} R _inst_1) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R η _inst_1 (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1) (fun (a : η) (b : η) => _inst_5 a b) i) (OfNat.ofNat.{u1} ((fun (i : η) => R) i) 1 (OfNat.mk.{u1} ((fun (i : η) => R) i) 1 (One.one.{u1} ((fun (i : η) => R) i) (AddMonoidWithOne.toOne.{u1} ((fun (i : η) => R) i) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))))))))
 but is expected to have type
-  forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (i : η), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (Basis.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) η (fun (_x : η) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) _x) (Basis.funLike.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) (Pi.basisFun.{u1, u2} R η _inst_1 _inst_4) i) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (η -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} η (fun (i : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => η -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (η -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} η (fun (i : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R η _inst_1 (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1) (fun (a : η) (b : η) => _inst_5 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+  forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (i : η), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (Basis.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) η (fun (_x : η) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) _x) (Basis.funLike.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) (Pi.basisFun.{u1, u2} R η _inst_1 _inst_4) i) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (η -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} η (fun (i : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => η -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (η -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} η (fun (i : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R η _inst_1 (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1) (fun (a : η) (b : η) => _inst_5 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align pi.basis_fun_apply Pi.basisFun_applyₓ'. -/
 @[simp]
 theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun i : η => R) i 1 := by
@@ -429,12 +429,18 @@ theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun
 lean 3 declaration is
   forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η] (x : η -> R) (i : η), Eq.{succ u1} R (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Finsupp.{u2, u1} η R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u2, u1} η R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) => η -> R) (Finsupp.coeFun.{u2, u1} η R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (η -> R) (Finsupp.{u2, u1} η R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (η -> R) (Finsupp.{u2, u1} η R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => (η -> R) -> (Finsupp.{u2, u1} η R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u2, u1} η R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{u2, u1} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Finsupp.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Basis.repr.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.basisFun.{u1, u2} R η _inst_1 _inst_4)) x) i) (x i)
 but is expected to have type
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(Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (η -> R) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (η -> R) (AddMonoid.toZero.{max u2 u1} (η -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => 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_inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddMonoid.toZero.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R 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_inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1))) (Module.toDistribMulAction.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)))))) (Basis.repr.{u1, u2, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Pi.basisFun.{u2, u1} R η _inst_1 _inst_4)) x) i) (x i)
+  forall (R : Type.{u2}) (η : Type.{u1}) [_inst_1 : Semiring.{u2} R] [_inst_4 : Fintype.{u1} η] (x : η -> R) (i : η), Eq.{succ u2} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : η) => R) i) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) η (fun (_x : η) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : η) => R) _x) (Finsupp.funLike.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (η -> R) (fun (_x : η -> R) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : η -> R) => Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _x) (SMulHomClass.toFunLike.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (η -> R) (AddMonoid.toZero.{max u2 u1} (η -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (η -> R) (AddMonoid.toAddZeroClass.{max u2 u1} (η -> R) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (η -> R) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddMonoid.toZero.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1))) (Module.toDistribMulAction.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)))))) (Basis.repr.{u1, u2, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Pi.basisFun.{u2, u1} R η _inst_1 _inst_4)) x) i) (x i)
 Case conversion may be inaccurate. Consider using '#align pi.basis_fun_repr Pi.basisFun_reprₓ'. -/
 @[simp]
 theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basis_fun]
 #align pi.basis_fun_repr Pi.basisFun_repr
 
+/- warning: pi.basis_fun_equiv_fun -> Pi.basisFun_equivFun is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η], Eq.{succ (max u2 u1)} (LinearEquiv.{u1, u1, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (η -> R) (η -> R) (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.addCommMonoid.{u2, u1} η (fun (ᾰ : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (Basis.equivFun.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) _inst_4 (Pi.basisFun.{u1, u2} R η _inst_1 _inst_4)) (LinearEquiv.refl.{u1, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)))
+but is expected to have type
+  forall (R : Type.{u2}) (η : Type.{u1}) [_inst_1 : Semiring.{u2} R] [_inst_4 : Fintype.{u1} η], Eq.{max (succ u2) (succ u1)} (LinearEquiv.{u2, u2, max u2 u1, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.addCommMonoid.{u1, u2} η (fun (ᾰ : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Pi.module.{u1, u2, u2} η (fun (a._@.Mathlib.LinearAlgebra.Basis._hyg.11185 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1))) (Basis.equivFun.{u1, u2, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) _inst_4 (Pi.basisFun.{u2, u1} R η _inst_1 _inst_4)) (LinearEquiv.refl.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)))
+Case conversion may be inaccurate. Consider using '#align pi.basis_fun_equiv_fun Pi.basisFun_equivFunₓ'. -/
 @[simp]
 theorem basisFun_equivFun : (Pi.basisFun R η).equivFun = LinearEquiv.refl _ _ :=
   Basis.equivFun_ofEquivFun _

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module linear_algebra.std_basis
-! leanprover-community/mathlib commit f8c79b0a623404854a2902b836eac32156fd7712
+! leanprover-community/mathlib commit 13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -435,6 +435,11 @@ Case conversion may be inaccurate. Consider using '#align pi.basis_fun_repr Pi.b
 theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basis_fun]
 #align pi.basis_fun_repr Pi.basisFun_repr
 
+@[simp]
+theorem basisFun_equivFun : (Pi.basisFun R η).equivFun = LinearEquiv.refl _ _ :=
+  Basis.equivFun_ofEquivFun _
+#align pi.basis_fun_equiv_fun Pi.basisFun_equivFun
+
 end
 
 end Module

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -61,7 +61,7 @@ def stdBasis : ∀ i : ι, φ i →ₗ[R] ∀ i, φ i :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{max (succ u2) (succ u3)} (forall (i : ι), φ i) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b) (Function.update.{succ u2, succ u3} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (OfNat.ofNat.{max u2 u3} (forall (a : ι), φ a) 0 (OfNat.mk.{max u2 u3} (forall (a : ι), φ a) 0 (Zero.zero.{max u2 u3} (forall (a : ι), φ a) (Pi.instZero.{u2, u3} ι (fun (a : ι) => φ a) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (φ i) (AddMonoid.toAddZeroClass.{u3} (φ i) (AddCommMonoid.toAddMonoid.{u3} (φ i) (_inst_2 i)))))))) i b)
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (b : φ i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : φ i) => forall (i : ι), φ i) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b) (Function.update.{succ u3, succ u2} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (OfNat.ofNat.{max u3 u2} (forall (a : ι), φ a) 0 (Zero.toOfNat0.{max u3 u2} (forall (a : ι), φ a) (Pi.instZero.{u3, u2} ι (fun (a : ι) => φ a) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i)))))) i b)
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (b : φ i), Eq.{max (succ u3) (succ u2)} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) b) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b) (Function.update.{succ u3, succ u2} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (OfNat.ofNat.{max u3 u2} (forall (a : ι), φ a) 0 (Zero.toOfNat0.{max u3 u2} (forall (a : ι), φ a) (Pi.instZero.{u3, u2} ι (fun (a : ι) => φ a) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i)))))) i b)
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_apply LinearMap.stdBasis_applyₓ'. -/
 theorem stdBasis_apply (i : ι) (b : φ i) : stdBasis R φ i b = update 0 i b :=
   rfl
@@ -71,7 +71,7 @@ theorem stdBasis_apply (i : ι) (b : φ i) : stdBasis R φ i b = update 0 i b :=
 lean 3 declaration is
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Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) (OfNat.ofNat.{u1} ((fun (_x : ι) => R) i) 1 (OfNat.mk.{u1} ((fun (_x : ι) => R) i) 1 (One.one.{u1} ((fun (_x : ι) => R) i) (AddMonoidWithOne.toOne.{u1} ((fun (_x : ι) => R) i) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))))))) i') (ite.{succ u1} ((fun (_x : ι) => R) i') (Eq.{succ u2} ι i i') (_inst_4 i i') (OfNat.ofNat.{u1} ((fun (_x : ι) => R) i') 1 (OfNat.mk.{u1} ((fun (_x : ι) => R) i') 1 (One.one.{u1} ((fun (_x : ι) => R) i') (AddMonoidWithOne.toOne.{u1} ((fun (_x : ι) => R) i') (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (_x : ι) => R) i') (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (_x : ι) => R) i') (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i') _inst_1))))))) (OfNat.ofNat.{u1} ((fun (_x : ι) => R) i') 0 (OfNat.mk.{u1} ((fun (_x : ι) => R) i') 0 (Zero.zero.{u1} ((fun (_x : ι) => R) i') (MulZeroClass.toHasZero.{u1} ((fun (_x : ι) => R) i') (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} ((fun (_x : ι) => R) i') (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i') (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i') _inst_1))))))))
 but is expected to have type
-  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] (i : ι) (i' : ι), Eq.{succ u2} R (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) i') (ite.{succ u2} R (Eq.{succ u1} ι i i') (_inst_4 i i') (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))
+  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] (i : ι) (i' : ι), Eq.{succ u2} R (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) i') (ite.{succ u2} R (Eq.{succ u1} ι i i') (_inst_4 i i') (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_apply' LinearMap.stdBasis_apply'ₓ'. -/
 @[simp]
 theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = ite (i = i') 1 0 :=
@@ -84,7 +84,7 @@ theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = i
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{max (succ u3) (succ (max u2 u3))} ((φ i) -> (forall (i : ι), φ i)) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Pi.single.{u2, u3} ι (fun (i : ι) => φ i) (fun (a : ι) (b : ι) => _inst_4 a b) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (φ i) (AddMonoid.toAddZeroClass.{u3} (φ i) (AddCommMonoid.toAddMonoid.{u3} (φ i) (_inst_2 i)))) i)
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : φ i), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : φ i) => forall (i : ι), φ i) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Pi.single.{u3, u2} ι φ (fun (a : ι) (b : ι) => _inst_4 a b) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i))) i)
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : φ i), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Pi.single.{u3, u2} ι φ (fun (a : ι) (b : ι) => _inst_4 a b) (fun (i : ι) => AddMonoid.toZero.{u2} (φ i) (AddCommMonoid.toAddMonoid.{u2} (φ i) (_inst_2 i))) i)
 Case conversion may be inaccurate. Consider using '#align linear_map.coe_std_basis LinearMap.coe_stdBasisₓ'. -/
 theorem coe_stdBasis (i : ι) : ⇑(stdBasis R φ i) = Pi.single i :=
   rfl
@@ -94,7 +94,7 @@ theorem coe_stdBasis (i : ι) : ⇑(stdBasis R φ i) = Pi.single i :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{succ u3} (φ i) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b i) b
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{succ u3} (φ i) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b i) b
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (b : φ i), Eq.{succ u3} (φ i) (FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b i) b
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_same LinearMap.stdBasis_sameₓ'. -/
 @[simp]
 theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
@@ -105,7 +105,7 @@ theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (j : ι), (Ne.{succ u2} ι j i) -> (forall (b : φ i), Eq.{succ u3} (φ j) (coeFn.{max (succ u3) (succ (max u2 u3)), max (succ u3) (succ (max u2 u3))} (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i))) => (φ i) -> (forall (i : ι), φ i)) (LinearMap.hasCoeToFun.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 ((fun (i : ι) => _inst_2 i) i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => (fun (i : ι) => _inst_2 i) i)) ((fun (i : ι) => _inst_3 i) i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => (fun (i : ι) => _inst_2 i) i) (fun (i : ι) => (fun (i : ι) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b j) (OfNat.ofNat.{u3} (φ j) 0 (OfNat.mk.{u3} (φ j) 0 (Zero.zero.{u3} (φ j) (AddZeroClass.toHasZero.{u3} (φ j) (AddMonoid.toAddZeroClass.{u3} (φ j) (AddCommMonoid.toAddMonoid.{u3} (φ j) (_inst_2 j))))))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (j : ι), (Ne.{succ u3} ι j i) -> (forall (b : φ i), Eq.{succ u2} (φ j) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b j) (OfNat.ofNat.{u2} (φ j) 0 (Zero.toOfNat0.{u2} (φ j) (AddMonoid.toZero.{u2} (φ j) (AddCommMonoid.toAddMonoid.{u2} (φ j) (_inst_2 j))))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (j : ι), (Ne.{succ u3} ι j i) -> (forall (b : φ i), Eq.{succ u2} (φ j) (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (φ i) (fun (_x : φ i) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : φ i) => forall (i : ι), φ i) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i) b j) (OfNat.ofNat.{u2} (φ j) 0 (Zero.toOfNat0.{u2} (φ j) (AddMonoid.toZero.{u2} (φ j) (AddCommMonoid.toAddMonoid.{u2} (φ j) (_inst_2 j))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_ne LinearMap.stdBasis_neₓ'. -/
 theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j = 0 :=
   Pi.single_eq_of_ne h b
@@ -128,7 +128,7 @@ theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι), Eq.{succ u3} (Submodule.{u1, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)) (LinearMap.ker.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Bot.bot.{u3} (Submodule.{u1, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)) (Submodule.hasBot.{u1, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)))
 but is expected to have type
-  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u1} ι] (i : ι), Eq.{succ u3} (Submodule.{u2, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)) (LinearMap.ker.{u2, u2, u3, max u1 u3, max u1 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u1, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u1, u3, u2} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u1, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u1, u3, u2} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, max u1 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u1, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u1, u3, u2} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Bot.bot.{u3} (Submodule.{u2, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)) (Submodule.instBotSubmodule.{u2, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)))
+  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u2, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u1} ι] (i : ι), Eq.{succ u3} (Submodule.{u2, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)) (LinearMap.ker.{u2, u2, u3, max u1 u3, max u1 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u1, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u1, u3, u2} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, max u1 u3} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u1, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u1, u3, u2} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u2, u2, u3, max u1 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u1, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u1, u3, u2} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)) (Bot.bot.{u3} (Submodule.{u2, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)) (Submodule.instBotSubmodule.{u2, u3} R (φ i) _inst_1 (_inst_2 i) (_inst_3 i)))
 Case conversion may be inaccurate. Consider using '#align linear_map.ker_std_basis LinearMap.ker_stdBasisₓ'. -/
 theorem ker_stdBasis (i : ι) : ker (stdBasis R φ i) = ⊥ :=
   ker_eq_bot_of_injective <| Pi.single_injective _ _
@@ -168,7 +168,7 @@ theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_projₓ'. -/
 theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
     (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
@@ -185,7 +185,7 @@ theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Finset.{u2} ι} {J : Set.{u2} ι}, (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Finset.{u3} ι} {J : Set.{u3} ι}, (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) (Finset.toSet.{u3} ι I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iInf.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u2, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u2 u3, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))) (iSup.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Finset.{u3} ι} {J : Set.{u3} ι}, (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) (Finset.toSet.{u3} ι I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iInf.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u2, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))) (iSup.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasisₓ'. -/
 theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
     (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
@@ -208,7 +208,7 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Set.{u2} ι} {J : Set.{u2} ι}, (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) I J)) -> (Set.Finite.{u2} ι I) -> (Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Set.{u3} ι} {J : Set.{u3} ι}, (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) I J)) -> (Set.Finite.{u3} ι I) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Set.{u3} ι} {J : Set.{u3} ι}, (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) I J)) -> (Set.Finite.{u3} ι I) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_projₓ'. -/
 theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
@@ -225,7 +225,7 @@ theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] [_inst_5 : Finite.{succ u2} ι], Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasTop.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] [_inst_5 : Finite.{succ u3} ι], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instTopSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] [_inst_5 : Finite.{succ u3} ι], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instTopSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
 Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis LinearMap.iSup_range_stdBasisₓ'. -/
 theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ :=
   by
@@ -242,7 +242,7 @@ theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (Disjoint.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.orderBot.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι 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_inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : 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i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasisₓ'. -/
 theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     Disjoint (⨆ i ∈ I, range (stdBasis R φ i)) (⨆ i ∈ J, range (stdBasis R φ i)) :=
@@ -265,7 +265,7 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
 lean 3 declaration is
   forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_4 : DecidableEq.{succ u2} ι] {a : R}, Eq.{max (succ u2) (succ u1)} (ι -> (forall (i : ι), (fun (_x : ι) => R) i)) (fun (i : ι) => coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i))) => R -> (forall (i : ι), (fun (_x : ι) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (_x : ι) => R) i) (forall (i : ι), (fun (_x : ι) => R) i) _inst_1 _inst_1 ((fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i)) ((fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} ι (fun (i : ι) => (fun (_x : ι) => R) i) R _inst_1 (fun (i : ι) => (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) i) (fun (i : ι) => (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u1} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) a) (fun (i : ι) => coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Finsupp.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (fun (_x : Finsupp.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) => ι -> R) (Finsupp.coeFun.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Finsupp.single.{u2, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) i a))
 but is expected to have type
-  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] {a : R}, Eq.{max (succ u2) (succ u1)} (ι -> ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => ι -> R) a)) (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) a) (fun (i : ι) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.single.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) i a))
+  forall (R : Type.{u2}) {ι : Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_4 : DecidableEq.{succ u1} ι] {a : R}, Eq.{max (succ u2) (succ u1)} (ι -> ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => ι -> R) a)) (fun (i : ι) => FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (LinearMap.{u2, u2, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) R (ι -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => ι -> R) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u2 u1} R R R (ι -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (Pi.addCommMonoid.{u1, u2} ι (fun (i : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1)))) (Semiring.toModule.{u2} R _inst_1) (Pi.module.{u1, u2, u2} ι (fun (i : ι) => R) R _inst_1 (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.2287 : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u1, u2} R ι _inst_1 (fun (_x : ι) => R) (fun (i : ι) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (_x : ι) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) (Semiring.toNonAssocSemiring.{u2} ((fun (_x : ι) => R) i) _inst_1))) (fun (i : ι) => Semiring.toModule.{u2} R _inst_1) (fun (a : ι) (b : ι) => _inst_4 a b) i) a) (fun (i : ι) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (Finsupp.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) ι (fun (_x : ι) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι) => R) _x) (Finsupp.funLike.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.single.{u1, u2} ι R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) i a))
 Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_eq_single LinearMap.stdBasis_eq_singleₓ'. -/
 theorem stdBasis_eq_single {a : R} :
     (fun i : ι => (stdBasis R (fun _ : ι => R) i) a) = fun i : ι => Finsupp.single i a :=
@@ -290,7 +290,7 @@ variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
 lean 3 declaration is
   forall {R : Type.{u1}} {η : Type.{u2}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u4}} [_inst_1 : Ring.{u1} R] [_inst_2 : forall (i : η), AddCommGroup.{u4} (Ms i)] [_inst_3 : forall (i : η), Module.{u1, u4} R (Ms i) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i))] [_inst_4 : DecidableEq.{succ u2} η] (v : forall (j : η), (ιs j) -> (Ms j)), (forall (i : η), LinearIndependent.{u3, u1, u4} (ιs i) R (Ms i) (v i) (Ring.toSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (_inst_3 i)) -> (LinearIndependent.{max u2 u3, u1, max u2 u4} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (forall (i : η), Ms i) (fun (ji : Sigma.{u2, u3} η (fun (j : η) => ιs j)) => coeFn.{max (succ u4) (succ (max u2 u4)), max (succ u4) (succ (max u2 u4))} (LinearMap.{u1, u1, u4, max u2 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) ((fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i)) ((fun (i : η) => _inst_3 i) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i) (fun (i : η) => (fun (i : η) => _inst_3 i) i))) (fun (_x : LinearMap.{u1, u1, u4, max u2 u4} R R (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) ((fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i)) ((fun (i : η) => _inst_3 i) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i) (fun (i : η) => (fun (i : η) => _inst_3 i) i))) => (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) -> (forall (i : η), Ms i)) (LinearMap.hasCoeToFun.{u1, u1, u4, max u2 u4} R R (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (Ring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R _inst_1) ((fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i)) ((fun (i : η) => _inst_3 i) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) i) (fun (i : η) => (fun (i : η) => _inst_3 i) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (LinearMap.stdBasis.{u1, u2, u4} R η (Ring.toSemiring.{u1} R _inst_1) Ms (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i) (fun (a : η) (b : η) => _inst_4 a b) (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji)) (v (Sigma.fst.{u2, u3} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u2, u3} η (fun (j : η) => ιs j) ji))) (Ring.toSemiring.{u1} R _inst_1) (Pi.addCommMonoid.{u2, u4} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i))) (Pi.module.{u2, u4, u1} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u1} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u4} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)))
 but is expected to have type
-  forall {R : Type.{u4}} {η : Type.{u2}} {ιs : η -> Type.{u1}} {Ms : η -> Type.{u3}} [_inst_1 : Ring.{u4} R] [_inst_2 : forall (i : η), AddCommGroup.{u3} (Ms i)] [_inst_3 : forall (i : η), Module.{u4, u3} R (Ms i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))] [_inst_4 : DecidableEq.{succ u2} η] (v : forall (j : η), (ιs j) -> (Ms j)), (forall (i : η), LinearIndependent.{u1, u4, u3} (ιs i) R (Ms i) (v i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (_inst_3 i)) -> (LinearIndependent.{max u2 u1, u4, max u2 u3} (Sigma.{u2, u1} η (fun (j : η) => ιs j)) R (forall (i : η), Ms i) (fun (ji : Sigma.{u2, u1} η (fun (j : η) => ιs j)) => FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u4, u4, u3, max u2 u3} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u2 u3} R R (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.stdBasis.{u4, u2, u3} R η (Ring.toSemiring.{u4} R _inst_1) Ms (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i) (fun (a : η) (b : η) => _inst_4 a b) (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (v (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u2, u1} η (fun (j : η) => ιs j) ji))) (Ring.toSemiring.{u4} R _inst_1) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)))
+  forall {R : Type.{u4}} {η : Type.{u2}} {ιs : η -> Type.{u1}} {Ms : η -> Type.{u3}} [_inst_1 : Ring.{u4} R] [_inst_2 : forall (i : η), AddCommGroup.{u3} (Ms i)] [_inst_3 : forall (i : η), Module.{u4, u3} R (Ms i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))] [_inst_4 : DecidableEq.{succ u2} η] (v : forall (j : η), (ιs j) -> (Ms j)), (forall (i : η), LinearIndependent.{u1, u4, u3} (ιs i) R (Ms i) (v i) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (_inst_3 i)) -> (LinearIndependent.{max u2 u1, u4, max u2 u3} (Sigma.{u2, u1} η (fun (j : η) => ιs j)) R (forall (i : η), Ms i) (fun (ji : Sigma.{u2, u1} η (fun (j : η) => ιs j)) => FunLike.coe.{max (succ u2) (succ u3), succ u3, max (succ u2) (succ u3)} (LinearMap.{u4, u4, u3, max u2 u3} R R (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1))) (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u2, u1} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u4, u4, u3, max u2 u3} R R (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (Ring.toSemiring.{u4} R _inst_1) (Ring.toSemiring.{u4} R _inst_1) (AddCommGroup.toAddCommMonoid.{u3} (Ms (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (_inst_2 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji))) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (_inst_3 (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (Ring.toSemiring.{u4} R _inst_1)))) (LinearMap.stdBasis.{u4, u2, u3} R η (Ring.toSemiring.{u4} R _inst_1) Ms (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i) (fun (a : η) (b : η) => _inst_4 a b) (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji)) (v (Sigma.fst.{u2, u1} η (fun (j : η) => ιs j) ji) (Sigma.snd.{u2, u1} η (fun (j : η) => ιs j) ji))) (Ring.toSemiring.{u4} R _inst_1) (Pi.addCommMonoid.{u2, u3} η (fun (i : η) => Ms i) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i))) (Pi.module.{u2, u3, u4} η (fun (i : η) => Ms i) R (Ring.toSemiring.{u4} R _inst_1) (fun (i : η) => AddCommGroup.toAddCommMonoid.{u3} (Ms i) (_inst_2 i)) (fun (i : η) => _inst_3 i)))
 Case conversion may be inaccurate. Consider using '#align pi.linear_independent_std_basis Pi.linearIndependent_stdBasisₓ'. -/
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
@@ -352,7 +352,7 @@ protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
 lean 3 declaration is
   forall {R : Type.{u1}} {η : Type.{u2}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : η), AddCommMonoid.{u4} (Ms i)] [_inst_3 : forall (i : η), Module.{u1, u4} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (s : forall (j : η), Basis.{u3, u1, u4} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (j : η) (i : ιs j), Eq.{max (succ (max u2 u3)) (succ u1)} (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{max (succ (max u2 u4)) (succ (max (max u2 u3) u1)), max (succ (max u2 u4)) (succ (max (max u2 u3) u1))} (LinearEquiv.{u1, u1, max u2 u4, max (max u2 u3) u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, max u2 u4, max (max u2 u3) u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => (forall (j : η), Ms j) -> (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (LinearEquiv.hasCoeToFun.{u1, u1, max u2 u4, max (max u2 u3) u1} R R (forall (j : η), Ms j) (Finsupp.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Finsupp.addCommMonoid.{max u2 u3, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u4, u1} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u2 u3, u1, u1} (Sigma.{u2, u3} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Basis.repr.{max u2 u3, u1, max 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 but is expected to have type
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j) (forall (i : η), Ms i) _inst_1 _inst_1 (_inst_2 j) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 j) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u4, u1} R η _inst_1 Ms (fun (i : η) => _inst_2 i) (fun (j : η) => _inst_3 j) (fun (a : η) (b : η) => _inst_5 a b) j) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ιs j) (fun (_x : ιs j) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ιs j) => Ms j) _x) (Basis.funLike.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (s j) i))) (Finsupp.single.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (Sigma.mk.{u4, u3} η (fun (j : η) => ιs j) j i) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align pi.basis_repr_std_basis Pi.basis_repr_stdBasisₓ'. -/
 @[simp]
 theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (j i) :
@@ -380,7 +380,7 @@ theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j))
 lean 3 declaration is
   forall {R : Type.{u1}} {η : Type.{u2}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u4}} [_inst_1 : Semiring.{u1} R] [_inst_2 : forall (i : η), AddCommMonoid.{u4} (Ms i)] [_inst_3 : forall (i : η), Module.{u1, u4} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (s : forall (j : η), Basis.{u3, u1, u4} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ji : Sigma.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j)), Eq.{max (succ u2) (succ u4)} (forall (j : η), (fun (j : η) => Ms j) j) (coeFn.{max (succ (max u2 u3)) (succ u1) (succ (max u2 u4)), max (succ (max u2 u3)) (succ (max u2 u4))} (Basis.{max u2 u3, u1, max u2 u4} (Sigma.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j)) R (forall (j : η), (fun (j : η) => Ms j) j) _inst_1 (Pi.addCommMonoid.{u2, u4} η (fun (j : η) => (fun (j : η) => Ms j) j) (fun (i : η) => (fun (j : η) => _inst_2 j) i)) (Pi.module.{u2, u4, u1} η (fun (j : η) => (fun (j : η) => Ms j) j) R _inst_1 (fun (i : η) => (fun (j : 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: η) => (fun (j : η) => ιs j) j) ji)) (coeFn.{max (succ u3) (succ u1) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u1, u4} (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) R (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) (_inst_3 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji))) (fun (_x : Basis.{u3, u1, u4} (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) R (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) (_inst_3 (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji))) => (ιs (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji)) -> (Ms (Sigma.fst.{u2, u3} η (fun (j : η) => (fun (j : η) => ιs j) j) ji))) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u4), succ u3, succ u4} 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=> (fun (j : η) => ιs j) j) ji)))
 but is expected to have type
-  forall {R : Type.{u2}} {η : Type.{u4}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : η), AddCommMonoid.{u1} (Ms i)] [_inst_3 : forall (i : η), Module.{u2, u1} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u4} η] [_inst_5 : DecidableEq.{succ u4} η] (s : forall (j : η), Basis.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)), Eq.{max (succ u4) (succ u1)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) ji) (FunLike.coe.{max (max (max (succ u2) (succ u4)) (succ u3)) (succ u1), max (succ u4) (succ u3), max (succ u4) (succ u1)} (Basis.{max u3 u4, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Sigma.{u4, u3} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) _x) (Basis.funLike.{max u4 u3, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Pi.basis.{u2, u4, u3, u1} R η (fun (j : η) => ιs j) (fun (j : η) => Ms j) _inst_1 (fun (j : η) => _inst_2 j) (fun (j : η) => _inst_3 j) _inst_4 s) ji) (FunLike.coe.{max (succ u4) (succ u1), succ u1, max (succ u4) (succ u1)} (LinearMap.{u2, u2, u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u4 u1} R R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u4, u1} R η _inst_1 Ms (fun (i : η) => _inst_2 i) (fun (j : η) => _inst_3 j) (fun (a : η) (b : η) => _inst_5 a b) (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (fun (_x : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _x) (Basis.funLike.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (s (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)))
+  forall {R : Type.{u2}} {η : Type.{u4}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : η), AddCommMonoid.{u1} (Ms i)] [_inst_3 : forall (i : η), Module.{u2, u1} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u4} η] [_inst_5 : DecidableEq.{succ u4} η] (s : forall (j : η), Basis.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (ji : Sigma.{u4, u3} η (fun (j : η) => ιs j)), Eq.{max (succ u4) (succ u1)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) ji) (FunLike.coe.{max (max (max (succ u2) (succ u4)) (succ u3)) (succ u1), max (succ u4) (succ u3), max (succ u4) (succ u1)} (Basis.{max u3 u4, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Sigma.{u4, u3} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Sigma.{u4, u3} η (fun (j : η) => ιs j)) => forall (j : η), Ms j) _x) (Basis.funLike.{max u4 u3, u2, max u4 u1} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (forall (j : η), Ms j) _inst_1 (Pi.addCommMonoid.{u4, u1} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i)) (Pi.module.{u4, u1, u2} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Pi.basis.{u2, u4, u3, u1} R η (fun (j : η) => ιs j) (fun (j : η) => Ms j) _inst_1 (fun (j : η) => _inst_2 j) (fun (j : η) => _inst_3 j) _inst_4 s) ji) (FunLike.coe.{max (succ u4) (succ u1), succ u1, max (succ u4) (succ u1)} (LinearMap.{u2, u2, u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i))) (Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) (fun (_x : Ms (Sigma.fst.{u4, u3} η (fun (i : η) => ιs i) ji)) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => forall (i : η), Ms i) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, max u4 u1} R R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (forall (i : η), Ms i) _inst_1 _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Pi.module.{u4, u1, u2} η (fun (i : η) => Ms i) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (LinearMap.stdBasis.{u2, u4, u1} R η _inst_1 Ms (fun (i : η) => _inst_2 i) (fun (j : η) => _inst_3 j) (fun (a : η) (b : η) => _inst_5 a b) (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), succ u3, succ u1} (Basis.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (fun (_x : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) => Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _x) (Basis.funLike.{u3, u2, u1} (ιs (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) R (Ms (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) _inst_1 (_inst_2 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (_inst_3 (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji))) (s (Sigma.fst.{u4, u3} η (fun (j : η) => ιs j) ji)) (Sigma.snd.{u4, u3} η (fun (j : η) => ιs j) ji)))
 Case conversion may be inaccurate. Consider using '#align pi.basis_apply Pi.basis_applyₓ'. -/
 @[simp]
 theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
@@ -417,7 +417,7 @@ noncomputable def basisFun : Basis η R (∀ j : η, R) :=
 lean 3 declaration is
   forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (i : η), Eq.{max (succ u2) (succ u1)} (η -> R) (coeFn.{max (succ u2) (succ u1) (succ (max u2 u1)), max (succ u2) (succ (max u2 u1))} (Basis.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : Basis.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) => η -> η -> R) (FunLike.hasCoeToFun.{max (succ u2) (succ u1) (succ (max u2 u1)), succ u2, succ (max u2 u1)} (Basis.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.Function.module.{u2, u1, u1} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) η (fun (_x : η) => η -> R) (Basis.funLike.{u2, u1, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η 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(fun (i : η) => R) i) (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i)) ((fun (i : η) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} η (fun (i : η) => (fun (i : η) => R) i) R _inst_1 (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (fun (i : η) => (fun (i : η) => Semiring.toModule.{u1} R _inst_1) i))) (fun (_x : LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) ((fun (i : η) => R) i) (forall (i : η), (fun (i : η) => R) i) ((fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => (fun (i : η) => R) i) (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i)) ((fun (i : η) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} η (fun (i : η) => (fun (i : η) => R) i) R _inst_1 (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (fun (i : η) => (fun (i : η) => Semiring.toModule.{u1} R _inst_1) i))) => R -> (forall (i : η), (fun (i : η) => R) i)) (LinearMap.hasCoeToFun.{u1, u1, u1, max u2 u1} R R ((fun (i : η) => R) i) (forall (i : η), (fun (i : η) => R) i) _inst_1 _inst_1 ((fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => (fun (i : η) => R) i) (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i)) ((fun (i : η) => Semiring.toModule.{u1} R _inst_1) i) (Pi.module.{u2, u1, u1} η (fun (i : η) => (fun (i : η) => R) i) R _inst_1 (fun (i : η) => (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) i) (fun (i : η) => (fun (i : η) => Semiring.toModule.{u1} R _inst_1) i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R η _inst_1 (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1) (fun (a : η) (b : η) => _inst_5 a b) i) (OfNat.ofNat.{u1} ((fun (i : η) => R) i) 1 (OfNat.mk.{u1} ((fun (i : η) => R) i) 1 (One.one.{u1} ((fun (i : η) => R) i) (AddMonoidWithOne.toOne.{u1} ((fun (i : η) => R) i) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))))))))
 but is expected to have type
-  forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (i : η), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (Basis.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) η (fun (_x : η) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) _x) (Basis.funLike.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) (Pi.basisFun.{u1, u2} R η _inst_1 _inst_4) i) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (η -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 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(Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => η -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (η -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} η (fun (i : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R η _inst_1 (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1) (fun (a : η) (b : η) => _inst_5 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
+  forall (R : Type.{u1}) (η : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_4 : Fintype.{u2} η] [_inst_5 : DecidableEq.{succ u2} η] (i : η), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) i) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (Basis.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) η (fun (_x : η) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : η) => η -> R) _x) (Basis.funLike.{u2, u1, max u1 u2} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u2, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{u2, u1, u1} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) (Pi.basisFun.{u1, u2} R η _inst_1 _inst_4) i) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (η -> R) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} η (fun (i : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => η -> R) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, max u1 u2} R R R (η -> R) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (Pi.addCommMonoid.{u2, u1} η (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Pi.module.{u2, u1, u1} η (fun (i : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3637 : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.stdBasis.{u1, u2, u1} R η _inst_1 (fun (i : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (i : η) => R) i) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (i : η) => R) i) (Semiring.toNonAssocSemiring.{u1} ((fun (i : η) => R) i) _inst_1))) (fun (i : η) => Semiring.toModule.{u1} R _inst_1) (fun (a : η) (b : η) => _inst_5 a b) i) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align pi.basis_fun_apply Pi.basisFun_applyₓ'. -/
 @[simp]
 theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun i : η => R) i 1 := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module linear_algebra.std_basis
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
+! leanprover-community/mathlib commit f8c79b0a623404854a2902b836eac32156fd7712
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,7 +19,7 @@ import Mathbin.LinearAlgebra.Pi
 > Any changes to this file require a corresponding PR to mathlib4.
 
 This file defines the standard basis `pi.basis (s : ∀ j, basis (ι j) R (M j))`,
-which is the `Σ j, ι j`-indexed basis of Π j, M j`. The basis vectors are given by
+which is the `Σ j, ι j`-indexed basis of `Π j, M j`. The basis vectors are given by
 `pi.basis s ⟨j, i⟩ j' = linear_map.std_basis R M j' (s j) i = if j = j' then s i else 0`.
 
 The standard basis on `R^η`, i.e. `η → R` is called `pi.basis_fun`.

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

@@ -166,7 +166,7 @@ theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ
 
 /- warning: linear_map.supr_range_std_basis_le_infi_ker_proj -> LinearMap.iSup_range_stdBasis_le_iInf_ker_proj is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, 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(fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 but is expected to have type
   forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_projₓ'. -/
@@ -183,7 +183,7 @@ theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
 
 /- warning: linear_map.infi_ker_proj_le_supr_range_std_basis -> LinearMap.iInf_ker_proj_le_iSup_range_stdBasis is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Finset.{u2} ι} {J : Set.{u2} ι}, (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Finset.{u2} ι} {J : Set.{u2} ι}, (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toHasLe.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 but is expected to have type
   forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Finset.{u3} ι} {J : Set.{u3} ι}, (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) (Finset.toSet.{u3} ι I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iInf.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u2, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u2 u3, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))) (iSup.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasisₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -164,30 +164,30 @@ theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ
   LinearMap.ext <| stdBasis_ne R φ _ _ h
 #align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_ne
 
-/- warning: linear_map.supr_range_std_basis_le_infi_ker_proj -> LinearMap.supᵢ_range_stdBasis_le_infᵢ_ker_proj is a dubious translation:
+/- warning: linear_map.supr_range_std_basis_le_infi_ker_proj -> LinearMap.iSup_range_stdBasis_le_iInf_ker_proj is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (supᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (infᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
-Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.supᵢ_range_stdBasis_le_infᵢ_ker_projₓ'. -/
-theorem supᵢ_range_stdBasis_le_infᵢ_ker_proj (I J : Set ι) (h : Disjoint I J) :
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_projₓ'. -/
+theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
     (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
   by
-  refine' supᵢ_le fun i => supᵢ_le fun hi => range_le_iff_comap.2 _
+  refine' iSup_le fun i => iSup_le fun hi => range_le_iff_comap.2 _
   simp only [(ker_comp _ _).symm, eq_top_iff, SetLike.le_def, mem_ker, comap_infi, mem_infi]
   rintro b - j hj
   rw [proj_std_basis_ne R φ j i, zero_apply]
   rintro rfl
   exact h.le_bot ⟨hi, hj⟩
-#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.supᵢ_range_stdBasis_le_infᵢ_ker_proj
+#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_proj
 
-/- warning: linear_map.infi_ker_proj_le_supr_range_std_basis -> LinearMap.infᵢ_ker_proj_le_supᵢ_range_stdBasis is a dubious translation:
+/- warning: linear_map.infi_ker_proj_le_supr_range_std_basis -> LinearMap.iInf_ker_proj_le_iSup_range_stdBasis is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Finset.{u2} ι} {J : Set.{u2} ι}, (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (infᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, 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i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) 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u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Finset.{u2} ι} {J : Set.{u2} ι}, (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} 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i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Finset.{u3} ι} {J : Set.{u3} ι}, (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) (Finset.toSet.{u3} ι I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (infᵢ.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u2, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u2 u3, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))) (supᵢ.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
-Case conversion may be inaccurate. Consider using '#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.infᵢ_ker_proj_le_supᵢ_range_stdBasisₓ'. -/
-theorem infᵢ_ker_proj_le_supᵢ_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Finset.{u3} ι} {J : Set.{u3} ι}, (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) (Finset.toSet.{u3} ι I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (iInf.{max u2 u3, succ u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) 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i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) 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+Case conversion may be inaccurate. Consider using '#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasisₓ'. -/
+theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
     (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
   SetLike.le_def.2
     (by
@@ -202,47 +202,47 @@ theorem infᵢ_ker_proj_le_supᵢ_range_stdBasis {I : Finset ι} {J : Set ι} (h
           rw [std_basis_same]
           exact hb _ ((hu trivial).resolve_left hiI)]
       exact sum_mem_bsupr fun i hi => mem_range_self (std_basis R φ i) (b i))
-#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.infᵢ_ker_proj_le_supᵢ_range_stdBasis
+#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasis
 
-/- warning: linear_map.supr_range_std_basis_eq_infi_ker_proj -> LinearMap.supᵢ_range_stdBasis_eq_infᵢ_ker_proj is a dubious translation:
+/- warning: linear_map.supr_range_std_basis_eq_infi_ker_proj -> LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj is a dubious translation:
 lean 3 declaration is
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_inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (infᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Set.{u2} ι} {J : Set.{u2} ι}, (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) I J)) -> (Set.Finite.{u2} ι I) -> (Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Set.{u3} ι} {J : Set.{u3} ι}, (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) I J)) -> (Set.Finite.{u3} ι I) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (infᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
-Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.supᵢ_range_stdBasis_eq_infᵢ_ker_projₓ'. -/
-theorem supᵢ_range_stdBasis_eq_infᵢ_ker_proj {I J : Set ι} (hd : Disjoint I J)
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Set.{u3} ι} {J : Set.{u3} ι}, (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) I J)) -> (Set.Finite.{u3} ι I) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iInf.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => iInf.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, max u3 u2, u2} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_projₓ'. -/
+theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
     (⨆ i ∈ I, range (stdBasis R φ i)) = ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
   by
   refine' le_antisymm (supr_range_std_basis_le_infi_ker_proj _ _ _ _ hd) _
   have : Set.univ ⊆ ↑hI.to_finset ∪ J := by rwa [hI.coe_to_finset]
-  refine' le_trans (infi_ker_proj_le_supr_range_std_basis R φ this) (supᵢ_mono fun i => _)
+  refine' le_trans (infi_ker_proj_le_supr_range_std_basis R φ this) (iSup_mono fun i => _)
   rw [Set.Finite.mem_toFinset]
   exact le_rfl
-#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.supᵢ_range_stdBasis_eq_infᵢ_ker_proj
+#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj
 
-/- warning: linear_map.supr_range_std_basis -> LinearMap.supᵢ_range_stdBasis is a dubious translation:
+/- warning: linear_map.supr_range_std_basis -> LinearMap.iSup_range_stdBasis is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] [_inst_5 : Finite.{succ u2} ι], Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasTop.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] [_inst_5 : Finite.{succ u2} ι], Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasTop.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] [_inst_5 : Finite.{succ u3} ι], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instTopSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
-Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis LinearMap.supᵢ_range_stdBasisₓ'. -/
-theorem supᵢ_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ :=
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] [_inst_5 : Finite.{succ u3} ι], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instTopSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
+Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis LinearMap.iSup_range_stdBasisₓ'. -/
+theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ :=
   by
   cases nonempty_fintype ι
   convert top_unique (infi_emptyset.ge.trans <| infi_ker_proj_le_supr_range_std_basis R φ _)
   ·
     exact
       funext fun i =>
-        ((@supᵢ_pos _ _ _ fun h => range <| std_basis R φ i) <| Finset.mem_univ i).symm
+        ((@iSup_pos _ _ _ fun h => range <| std_basis R φ i) <| Finset.mem_univ i).symm
   · rw [Finset.coe_univ, Set.union_empty]
-#align linear_map.supr_range_std_basis LinearMap.supᵢ_range_stdBasis
+#align linear_map.supr_range_std_basis LinearMap.iSup_range_stdBasis
 
 /- warning: linear_map.disjoint_std_basis_std_basis -> LinearMap.disjoint_stdBasis_stdBasis is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (Disjoint.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.orderBot.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (supᵢ.{max u2 u3, succ u2} 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=> _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (Disjoint.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.orderBot.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iSup.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 but is expected to have type
-  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (iSup.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => iSup.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
 Case conversion may be inaccurate. Consider using '#align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasisₓ'. -/
 theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     Disjoint (⨆ i ∈ I, range (stdBasis R φ i)) (⨆ i ∈ J, range (stdBasis R φ i)) :=
@@ -300,9 +300,9 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
     by
     intro j
     exact (hs j).map' _ (ker_std_basis _ _ _)
-  apply linearIndependent_unionᵢ_finite hs'
+  apply linearIndependent_iUnion_finite hs'
   · intro j J _ hiJ
-    simp [(Set.unionᵢ.equations._eqn_1 _).symm, Submodule.span_image, Submodule.span_unionᵢ]
+    simp [(Set.iUnion.equations._eqn_1 _).symm, Submodule.span_image, Submodule.span_iUnion]
     have h₀ :
       ∀ j, span R (range fun i : ιs j => std_basis R Ms j (v j i)) ≤ range (std_basis R Ms j) :=
       by
@@ -313,12 +313,12 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
       span R (range fun i : ιs j => std_basis R Ms j (v j i)) ≤
         ⨆ i ∈ {j}, range (std_basis R Ms i) :=
       by
-      rw [@supᵢ_singleton _ _ _ fun i => LinearMap.range (std_basis R (fun j : η => Ms j) i)]
+      rw [@iSup_singleton _ _ _ fun i => LinearMap.range (std_basis R (fun j : η => Ms j) i)]
       apply h₀
     have h₂ :
       (⨆ j ∈ J, span R (range fun i : ιs j => std_basis R Ms j (v j i))) ≤
         ⨆ j ∈ J, range (std_basis R (fun j : η => Ms j) j) :=
-      supᵢ₂_mono fun i _ => h₀ i
+      iSup₂_mono fun i _ => h₀ i
     have h₃ : Disjoint (fun i : η => i ∈ {j}) J := by
       convert Set.disjoint_singleton_left.2 hiJ using 0
     exact (disjoint_std_basis_std_basis _ _ _ _ h₃).mono h₁ h₂

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module linear_algebra.std_basis
-! leanprover-community/mathlib commit f2edd790f6c6e1d660515f76768f63cb717434d7
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.Pi
 /-!
 # The standard basis
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the standard basis `pi.basis (s : ∀ j, basis (ι j) R (M j))`,
 which is the `Σ j, ι j`-indexed basis of Π j, M j`. The basis vectors are given by
 `pi.basis s ⟨j, i⟩ j' = linear_map.std_basis R M j' (s j) i = if j = j' then s i else 0`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -47,15 +47,29 @@ namespace LinearMap
 variable (R : Type _) {ι : Type _} [Semiring R] (φ : ι → Type _) [∀ i, AddCommMonoid (φ i)]
   [∀ i, Module R (φ i)] [DecidableEq ι]
 
+#print LinearMap.stdBasis /-
 /-- The standard basis of the product of `φ`. -/
 def stdBasis : ∀ i : ι, φ i →ₗ[R] ∀ i, φ i :=
   single
 #align linear_map.std_basis LinearMap.stdBasis
+-/
 
+/- warning: linear_map.std_basis_apply -> LinearMap.stdBasis_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_apply LinearMap.stdBasis_applyₓ'. -/
 theorem stdBasis_apply (i : ι) (b : φ i) : stdBasis R φ i b = update 0 i b :=
   rfl
 #align linear_map.std_basis_apply LinearMap.stdBasis_apply
 
+/- warning: linear_map.std_basis_apply' -> LinearMap.stdBasis_apply' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_apply' LinearMap.stdBasis_apply'ₓ'. -/
 @[simp]
 theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = ite (i = i') 1 0 :=
   by
@@ -63,19 +77,43 @@ theorem stdBasis_apply' (i i' : ι) : (stdBasis R (fun _x : ι => R) i) 1 i' = i
   congr 1; rw [eq_iff_iff, eq_comm]
 #align linear_map.std_basis_apply' LinearMap.stdBasis_apply'
 
+/- warning: linear_map.coe_std_basis -> LinearMap.coe_stdBasis is a dubious translation:
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 theorem coe_stdBasis (i : ι) : ⇑(stdBasis R φ i) = Pi.single i :=
   rfl
 #align linear_map.coe_std_basis LinearMap.coe_stdBasis
 
+/- warning: linear_map.std_basis_same -> LinearMap.stdBasis_same is a dubious translation:
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 @[simp]
 theorem stdBasis_same (i : ι) (b : φ i) : stdBasis R φ i b i = b :=
   Pi.single_eq_same i b
 #align linear_map.std_basis_same LinearMap.stdBasis_same
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_ne LinearMap.stdBasis_neₓ'. -/
 theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j = 0 :=
   Pi.single_eq_of_ne h b
 #align linear_map.std_basis_ne LinearMap.stdBasis_ne
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_eq_pi_diag LinearMap.stdBasis_eq_pi_diagₓ'. -/
 theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   by
   ext (x j)
@@ -83,22 +121,52 @@ theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   rfl
 #align linear_map.std_basis_eq_pi_diag LinearMap.stdBasis_eq_pi_diag
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.ker_std_basis LinearMap.ker_stdBasisₓ'. -/
 theorem ker_stdBasis (i : ι) : ker (stdBasis R φ i) = ⊥ :=
   ker_eq_bot_of_injective <| Pi.single_injective _ _
 #align linear_map.ker_std_basis LinearMap.ker_stdBasis
 
+/- warning: linear_map.proj_comp_std_basis -> LinearMap.proj_comp_stdBasis is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.proj_comp_std_basis LinearMap.proj_comp_stdBasisₓ'. -/
 theorem proj_comp_stdBasis (i j : ι) : (proj i).comp (stdBasis R φ j) = diag j i := by
   rw [std_basis_eq_pi_diag, proj_pi]
 #align linear_map.proj_comp_std_basis LinearMap.proj_comp_stdBasis
 
+/- warning: linear_map.proj_std_basis_same -> LinearMap.proj_stdBasis_same is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align linear_map.proj_std_basis_same LinearMap.proj_stdBasis_sameₓ'. -/
 theorem proj_stdBasis_same (i : ι) : (proj i).comp (stdBasis R φ i) = id :=
   LinearMap.ext <| stdBasis_same R φ i
 #align linear_map.proj_std_basis_same LinearMap.proj_stdBasis_same
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_neₓ'. -/
 theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ j) = 0 :=
   LinearMap.ext <| stdBasis_ne R φ _ _ h
 #align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_ne
 
+/- warning: linear_map.supr_range_std_basis_le_infi_ker_proj -> LinearMap.supᵢ_range_stdBasis_le_infᵢ_ker_proj is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (I : Set.{u2} ι) (J : Set.{u2} ι), (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteSemilatticeInf.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toCompleteSemilatticeInf.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (supᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) 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(Set.hasMem.{u2} ι) i I) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (infᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+but is expected to have type
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (LE.le.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 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+Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.supᵢ_range_stdBasis_le_infᵢ_ker_projₓ'. -/
 theorem supᵢ_range_stdBasis_le_infᵢ_ker_proj (I J : Set ι) (h : Disjoint I J) :
     (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
   by
@@ -110,6 +178,12 @@ theorem supᵢ_range_stdBasis_le_infᵢ_ker_proj (I J : Set ι) (h : Disjoint I
   exact h.le_bot ⟨hi, hj⟩
 #align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.supᵢ_range_stdBasis_le_infᵢ_ker_proj
 
+/- warning: linear_map.infi_ker_proj_le_supr_range_std_basis -> LinearMap.infᵢ_ker_proj_le_supᵢ_range_stdBasis is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Finset.{u3} ι} {J : Set.{u3} ι}, (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) (Finset.toSet.{u3} ι I) J)) -> (LE.le.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Preorder.toLE.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (PartialOrder.toPreorder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 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i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+Case conversion may be inaccurate. Consider using '#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.infᵢ_ker_proj_le_supᵢ_range_stdBasisₓ'. -/
 theorem infᵢ_ker_proj_le_supᵢ_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
     (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
   SetLike.le_def.2
@@ -127,6 +201,12 @@ theorem infᵢ_ker_proj_le_supᵢ_range_stdBasis {I : Finset ι} {J : Set ι} (h
       exact sum_mem_bsupr fun i hi => mem_range_self (std_basis R φ i) (b i))
 #align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.infᵢ_ker_proj_le_supᵢ_range_stdBasis
 
+/- warning: linear_map.supr_range_std_basis_eq_infi_ker_proj -> LinearMap.supᵢ_range_stdBasis_eq_infᵢ_ker_proj is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] {I : Set.{u2} ι} {J : Set.{u2} ι}, (Disjoint.{u2} (Set.{u2} ι) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} ι) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} ι) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} ι) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} ι) (Set.completeBooleanAlgebra.{u2} ι)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u2} (Set.{u2} ι) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u2} (Set.{u2} ι) (Set.booleanAlgebra.{u2} ι))) I J) -> (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) (Set.univ.{u2} ι) (Union.union.{u2} (Set.{u2} ι) (Set.hasUnion.{u2} ι) I J)) -> (Set.Finite.{u2} ι I) -> (Eq.{succ (max u2 u3)} 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ι) (b : ι) => _inst_4 a b) i)))) (infᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasInf.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.ker.{u1, u1, max u2 u3, u3, max u2 u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, max u2 u3, u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (forall (i : ι), φ i) (φ i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i)) (LinearMap.semilinearMapClass.{u1, u1, max u2 u3, u3} R R (forall (i : ι), φ i) (φ i) _inst_1 _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_2 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u2, u3} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+but is expected to have type
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] {I : Set.{u3} ι} {J : Set.{u3} ι}, (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (HasSubset.Subset.{u3} (Set.{u3} ι) (Set.instHasSubsetSet.{u3} ι) (Set.univ.{u3} ι) (Union.union.{u3} (Set.{u3} ι) (Set.instUnionSet.{u3} ι) I J)) -> (Set.Finite.{u3} ι I) -> (Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 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(forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) ι (fun (i : ι) => infᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instInfSetSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.ker.{u1, u1, max u3 u2, u2, max u3 u2} R R 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i)) (_inst_3 i) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearMap.proj.{u1, u3, u2} R ι _inst_1 (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) i)))))
+Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.supᵢ_range_stdBasis_eq_infᵢ_ker_projₓ'. -/
 theorem supᵢ_range_stdBasis_eq_infᵢ_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
     (⨆ i ∈ I, range (stdBasis R φ i)) = ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) :=
@@ -138,6 +218,12 @@ theorem supᵢ_range_stdBasis_eq_infᵢ_ker_proj {I J : Set ι} (hd : Disjoint I
   exact le_rfl
 #align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.supᵢ_range_stdBasis_eq_infᵢ_ker_proj
 
+/- warning: linear_map.supr_range_std_basis -> LinearMap.supᵢ_range_stdBasis is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {ι : Type.{u2}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u3}) [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u3} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] [_inst_5 : Finite.{succ u2} ι], Eq.{succ (max u2 u3)} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u2 u3, succ u2} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.hasTop.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
+but is expected to have type
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] [_inst_5 : Finite.{succ u3} ι], Eq.{max (succ u3) (succ u2)} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i))) (Top.top.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.instTopSubmodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))
+Case conversion may be inaccurate. Consider using '#align linear_map.supr_range_std_basis LinearMap.supᵢ_range_stdBasisₓ'. -/
 theorem supᵢ_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ :=
   by
   cases nonempty_fintype ι
@@ -149,6 +235,12 @@ theorem supᵢ_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = 
   · rw [Finset.coe_univ, Set.union_empty]
 #align linear_map.supr_range_std_basis LinearMap.supᵢ_range_stdBasis
 
+/- warning: linear_map.disjoint_std_basis_std_basis -> LinearMap.disjoint_stdBasis_stdBasis is a dubious translation:
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=> _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u2 u3, 0} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toHasSup.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u2 u3} (Submodule.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u2 u3} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i J) => LinearMap.range.{u1, u1, u3, max u2 u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u3, max u2 u3} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.semilinearMapClass.{u1, u1, u3, max u2 u3} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u2, u3, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u2, u3} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+but is expected to have type
+  forall (R : Type.{u1}) {ι : Type.{u3}} [_inst_1 : Semiring.{u1} R] (φ : ι -> Type.{u2}) [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (φ i)] [_inst_3 : forall (i : ι), Module.{u1, u2} R (φ i) _inst_1 (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (I : Set.{u3} ι) (J : Set.{u3} ι), (Disjoint.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) (BoundedOrder.toOrderBot.{u3} (Set.{u3} ι) (Preorder.toLE.{u3} (Set.{u3} ι) (PartialOrder.toPreorder.{u3} (Set.{u3} ι) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} ι) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))))) (CompleteLattice.toBoundedOrder.{u3} (Set.{u3} ι) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} ι) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} ι) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} ι) (Set.instCompleteBooleanAlgebraSet.{u3} ι)))))) I J) -> (Disjoint.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (OmegaCompletePartialOrder.toPartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.instOmegaCompletePartialOrder.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Submodule.instOrderBotSubmoduleToLEToPreorderInstPartialOrderSetLike.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i I) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))) (supᵢ.{max u3 u2, succ u3} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) ι (fun (i : ι) => supᵢ.{max u3 u2, 0} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (ConditionallyCompleteLattice.toSupSet.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (CompleteLattice.toConditionallyCompleteLattice.{max u3 u2} (Submodule.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (Submodule.completeLattice.{u1, max u3 u2} R (forall (i : ι), φ i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))))) (Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) (fun (H : Membership.mem.{u3, u3} ι (Set.{u3} ι) (Set.instMembershipSet.{u3} ι) i J) => LinearMap.range.{u1, u1, u2, max u3 u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, max u3 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (φ i) (forall (i : ι), φ i) (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, max u3 u2} R R (φ i) (forall (i : ι), φ i) _inst_1 _inst_1 (_inst_2 i) (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => φ i) (fun (i : ι) => _inst_2 i)) (_inst_3 i) (Pi.module.{u3, u2, u1} ι (fun (i : ι) => φ i) R _inst_1 (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R _inst_1) (LinearMap.stdBasis.{u1, u3, u2} R ι _inst_1 φ (fun (i : ι) => _inst_2 i) (fun (i : ι) => _inst_3 i) (fun (a : ι) (b : ι) => _inst_4 a b) i)))))
+Case conversion may be inaccurate. Consider using '#align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasisₓ'. -/
 theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     Disjoint (⨆ i ∈ I, range (stdBasis R φ i)) (⨆ i ∈ J, range (stdBasis R φ i)) :=
   by
@@ -166,6 +258,12 @@ theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     · exact hI i hiI
 #align linear_map.disjoint_std_basis_std_basis LinearMap.disjoint_stdBasis_stdBasis
 
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+Case conversion may be inaccurate. Consider using '#align linear_map.std_basis_eq_single LinearMap.stdBasis_eq_singleₓ'. -/
 theorem stdBasis_eq_single {a : R} :
     (fun i : ι => (stdBasis R (fun _ : ι => R) i) a) = fun i : ι => Finsupp.single i a :=
   funext fun i => (Finsupp.single_eq_pi_single i a).symm
@@ -185,6 +283,12 @@ section Module
 
 variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
 
+/- warning: pi.linear_independent_std_basis -> Pi.linearIndependent_stdBasis is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align pi.linear_independent_std_basis Pi.linearIndependent_stdBasisₓ'. -/
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
     LinearIndependent R fun ji : Σj, ιs j => stdBasis R Ms ji.1 (v ji.1 ji.2) :=
@@ -225,6 +329,7 @@ section
 
 open LinearEquiv
 
+#print Pi.basis /-
 /-- `pi.basis (s : ∀ j, basis (ιs j) R (Ms j))` is the `Σ j, ιs j`-indexed basis on `Π j, Ms j`
 given by `s j` on each component.
 
@@ -238,7 +343,14 @@ protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
   refine' Basis.ofRepr (_ ≪≫ₗ (Finsupp.sigmaFinsuppLEquivPiFinsupp R).symm)
   exact LinearEquiv.piCongrRight fun j => (s j).repr
 #align pi.basis Pi.basis
+-/
 
+/- warning: pi.basis_repr_std_basis -> Pi.basis_repr_stdBasis is a dubious translation:
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+  forall {R : Type.{u2}} {η : Type.{u4}} {ιs : η -> Type.{u3}} {Ms : η -> Type.{u1}} [_inst_1 : Semiring.{u2} R] [_inst_2 : forall (i : η), AddCommMonoid.{u1} (Ms i)] [_inst_3 : forall (i : η), Module.{u2, u1} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u4} η] [_inst_5 : DecidableEq.{succ u4} η] (s : forall (j : η), Basis.{u3, u2, u1} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (j : η) (i : ιs j), Eq.{max (max (succ u2) (succ u4)) (succ u3)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : forall (j : η), Ms j) => Finsupp.{max u4 u3, u2} (Sigma.{u4, u3} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (FunLike.coe.{max (succ u1) (succ u4), succ u1, max (succ u1) (succ u4)} (LinearMap.{u2, u2, u1, max u4 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (Ms j) (forall (i : η), Ms i) (_inst_2 j) (Pi.addCommMonoid.{u4, u1} η (fun (i : η) => Ms i) (fun (i : η) => _inst_2 i)) 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+Case conversion may be inaccurate. Consider using '#align pi.basis_repr_std_basis Pi.basis_repr_stdBasisₓ'. -/
 @[simp]
 theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (j i) :
     (Pi.basis s).repr (stdBasis R _ j (s j i)) = Finsupp.single ⟨j, i⟩ 1 :=
@@ -261,12 +373,24 @@ theorem basis_repr_stdBasis [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j))
   contradiction
 #align pi.basis_repr_std_basis Pi.basis_repr_stdBasis
 
+/- warning: pi.basis_apply -> Pi.basis_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align pi.basis_apply Pi.basis_applyₓ'. -/
 @[simp]
 theorem basis_apply [DecidableEq η] (s : ∀ j, Basis (ιs j) R (Ms j)) (ji) :
     Pi.basis s ji = stdBasis R _ ji.1 (s ji.1 ji.2) :=
   Basis.apply_eq_iff.mpr (by simp)
 #align pi.basis_apply Pi.basis_apply
 
+/- warning: pi.basis_repr -> Pi.basis_repr is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u3}} {η : Type.{u1}} {ιs : η -> Type.{u4}} {Ms : η -> Type.{u2}} [_inst_1 : Semiring.{u3} R] [_inst_2 : forall (i : η), AddCommMonoid.{u2} (Ms i)] [_inst_3 : forall (i : η), Module.{u3, u2} R (Ms i) _inst_1 (_inst_2 i)] [_inst_4 : Fintype.{u1} η] (s : forall (j : η), Basis.{u4, u3, u2} (ιs j) R (Ms j) _inst_1 (_inst_2 j) (_inst_3 j)) (x : forall (j : η), Ms j) (ji : Sigma.{u1, u4} η (fun (j : η) => ιs j)), Eq.{succ u3} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u4} η (fun (j : η) => ιs j)) => R) ji) (FunLike.coe.{max (succ (max u1 u4)) (succ u3), succ (max u1 u4), succ u3} (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Sigma.{u1, u4} η (fun (j : η) => ιs j)) (fun (_x : Sigma.{u1, u4} η (fun (j : η) => ιs j)) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Sigma.{u1, u4} η (fun (j : η) => ιs j)) => R) _x) (Finsupp.funLike.{max u1 u4, u3} (Sigma.{u1, 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(DistribSMul.toSMulZeroClass.{u3, max (max u3 u1) u4} R (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (AddMonoid.toAddZeroClass.{max (max u3 u1) u4} (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u4} (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (Finsupp.addCommMonoid.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u3, max (max u3 u1) u4} R (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1)))) (Pi.module.{u1, u2, u3} η (fun (j : η) => Ms j) R _inst_1 (fun (i : η) => _inst_2 i) (fun (i : η) => _inst_3 i)) (Finsupp.module.{max u1 u4, u3, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_1))) (Semiring.toModule.{u3} R _inst_1))) R (forall (j : η), Ms j) (Finsupp.{max u1 u4, u3} (Sigma.{u1, u4} η (fun (j : η) => ιs j)) R (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1))) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u1 u2} (forall (j : η), Ms j) (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => Ms j) (fun (i : η) => _inst_2 i))) (AddCommMonoid.toAddMonoid.{max (max u3 u1) u4} (Finsupp.{max u1 u4, u3} 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+Case conversion may be inaccurate. Consider using '#align pi.basis_repr Pi.basis_reprₓ'. -/
 @[simp]
 theorem basis_repr (s : ∀ j, Basis (ιs j) R (Ms j)) (x) (ji) :
     (Pi.basis s).repr x ji = (s ji.1).repr (x ji.1) ji.2 :=
@@ -279,17 +403,31 @@ section
 
 variable (R η)
 
+#print Pi.basisFun /-
 /-- The basis on `η → R` where the `i`th basis vector is `function.update 0 i 1`. -/
 noncomputable def basisFun : Basis η R (∀ j : η, R) :=
   Basis.ofEquivFun (LinearEquiv.refl _ _)
 #align pi.basis_fun Pi.basisFun
+-/
 
+/- warning: pi.basis_fun_apply -> Pi.basisFun_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align pi.basis_fun_apply Pi.basisFun_applyₓ'. -/
 @[simp]
 theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun i : η => R) i 1 := by
   simp only [basis_fun, Basis.coe_ofEquivFun, LinearEquiv.refl_symm, LinearEquiv.refl_apply,
     std_basis_apply]
 #align pi.basis_fun_apply Pi.basisFun_apply
 
+/- warning: pi.basis_fun_repr -> Pi.basisFun_repr is a dubious translation:
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_inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)))))) (SMulZeroClass.toSMul.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddMonoid.toZero.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddMonoid.toAddZeroClass.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u2, max u2 u1, max u2 u1} (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{max u2 u1} (η -> R) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (AddCommMonoid.toAddMonoid.{max u2 u1} (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, max u2 u1} R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1))) (Module.toDistribMulAction.{u2, max u2 u1} R (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u2, max u2 u1, max u2 u1, max u2 u1} R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, max u2 u1, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (LinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, max u2 u1, max u2 u1} R R (η -> R) (Finsupp.{u1, u2} η R (MonoidWithZero.toZero.{u2} R (Semiring.toMonoidWithZero.{u2} R _inst_1))) _inst_1 _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Finsupp.addCommMonoid.{u1, u2} η R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Finsupp.module.{u1, u2, u2} η R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (Semiring.toModule.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)) (RingHomInvPair.ids.{u2} R _inst_1) (RingHomInvPair.ids.{u2} R _inst_1)))))) (Basis.repr.{u1, u2, max u2 u1} η R (η -> R) _inst_1 (Pi.addCommMonoid.{u1, u2} η (fun (j : η) => R) (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1)))) (Pi.module.{u1, u2, u2} η (fun (x._@.Mathlib.LinearAlgebra.StdBasis._hyg.3573 : η) => R) R _inst_1 (fun (i : η) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R _inst_1))) (fun (i : η) => Semiring.toModule.{u2} R _inst_1)) (Pi.basisFun.{u2, u1} R η _inst_1 _inst_4)) x) i) (x i)
+Case conversion may be inaccurate. Consider using '#align pi.basis_fun_repr Pi.basisFun_reprₓ'. -/
 @[simp]
 theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basis_fun]
 #align pi.basis_fun_repr Pi.basisFun_repr
@@ -304,13 +442,16 @@ namespace Matrix
 
 variable (R : Type _) (m n : Type _) [Fintype m] [Fintype n] [Semiring R]
 
+#print Matrix.stdBasis /-
 /-- The standard basis of `matrix m n R`. -/
 noncomputable def stdBasis : Basis (m × n) R (Matrix m n R) :=
   Basis.reindex (Pi.basis fun i : m => Pi.basisFun R n) (Equiv.sigmaEquivProd _ _)
 #align matrix.std_basis Matrix.stdBasis
+-/
 
 variable {n m}
 
+#print Matrix.stdBasis_eq_stdBasisMatrix /-
 theorem stdBasis_eq_stdBasisMatrix (i : n) (j : m) [DecidableEq n] [DecidableEq m] :
     stdBasis R n m (i, j) = stdBasisMatrix i j (1 : R) :=
   by
@@ -321,6 +462,7 @@ theorem stdBasis_eq_stdBasisMatrix (i : n) (j : m) [DecidableEq n] [DecidableEq
   · simp [std_basis, hi, hj, Ne.symm hi, LinearMap.stdBasis_ne]
   · simp [std_basis, hi, hj, Ne.symm hj, Ne.symm hi, LinearMap.stdBasis_ne]
 #align matrix.std_basis_eq_std_basis_matrix Matrix.stdBasis_eq_stdBasisMatrix
+-/
 
 end Matrix
 

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

@@ -235,7 +235,7 @@ protected noncomputable def basis (s : ∀ j, Basis (ιs j) R (Ms j)) :
   by
   -- The `add_comm_monoid (Π j, Ms j)` instance was hard to find.
   -- Defining this in tactic mode seems to shake up instance search enough that it works by itself.
-  refine' Basis.of_repr (_ ≪≫ₗ (Finsupp.sigmaFinsuppLEquivPiFinsupp R).symm)
+  refine' Basis.ofRepr (_ ≪≫ₗ (Finsupp.sigmaFinsuppLEquivPiFinsupp R).symm)
   exact LinearEquiv.piCongrRight fun j => (s j).repr
 #align pi.basis Pi.basis
 

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

@@ -79,7 +79,7 @@ theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j =
 theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) :=
   by
   ext (x j)
-  convert (update_apply 0 x i j _).symm
+  convert(update_apply 0 x i j _).symm
   rfl
 #align linear_map.std_basis_eq_pi_diag LinearMap.stdBasis_eq_pi_diag
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

@@ -193,7 +193,7 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
     by
     intro j
     exact (hs j).map' _ (ker_std_basis _ _ _)
-  apply linearIndependent_Union_finite hs'
+  apply linearIndependent_unionᵢ_finite hs'
   · intro j J _ hiJ
     simp [(Set.unionᵢ.equations._eqn_1 _).symm, Submodule.span_image, Submodule.span_unionᵢ]
     have h₀ :

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

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

• In lines I was modifying anyway, I also converted => to ↦.
• Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
• Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

@@ -18,7 +18,7 @@ which is the `Σ j, ι j`-indexed basis of `Π j, M j`. The basis vectors are gi
 
 The standard basis on `R^η`, i.e. `η → R` is called `Pi.basisFun`.
 
-To give a concrete example, `LinearMap.stdBasis R (λ (i : Fin 3), R) i 1`
+To give a concrete example, `LinearMap.stdBasis R (fun (i : Fin 3) ↦ R) i 1`
 gives the `i`th unit basis vector in `R³`, and `Pi.basisFun R (Fin 3)` proves
 this is a basis over `Fin 3 → R`.
 

@@ -299,13 +299,14 @@ end Pi
 
 namespace Module
 
-variable (ι R M N : Type*) [Fintype ι] [CommSemiring R]
+variable (ι R M N : Type*) [Finite ι] [CommSemiring R]
   [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R N]
 
 /-- The natural linear equivalence: `Mⁱ ≃ Hom(Rⁱ, M)` for an `R`-module `M`. -/
 noncomputable def piEquiv : (ι → M) ≃ₗ[R] ((ι → R) →ₗ[R] M) := Basis.constr (Pi.basisFun R ι) R
 
-lemma piEquiv_apply_apply (v : ι → M) (w : ι → R) :
+lemma piEquiv_apply_apply (ι R M : Type*) [Fintype ι] [CommSemiring R]
+    [AddCommMonoid M] [Module R M] (v : ι → M) (w : ι → R) :
     piEquiv ι R M v w = ∑ i, w i • v i := by
   simp only [piEquiv, Basis.constr_apply_fintype, Basis.equivFun_apply]
   congr

@@ -204,9 +204,9 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
 
 variable [Semiring R] [∀ i, AddCommMonoid (Ms i)] [∀ i, Module R (Ms i)]
 
-variable [Fintype η]
+section Fintype
 
-section
+variable [Fintype η]
 
 open LinearEquiv
 
@@ -264,10 +264,11 @@ theorem basis_repr (s : ∀ j, Basis (ιs j) R (Ms j)) (x) (ji) :
   rfl
 #align pi.basis_repr Pi.basis_repr
 
-end
+end Fintype
 
 section
 
+variable [Finite η]
 variable (R η)
 
 /-- The basis on `η → R` where the `i`th basis vector is `Function.update 0 i 1`. -/
@@ -321,7 +322,7 @@ end Module
 
 namespace Matrix
 
-variable (R : Type*) (m n : Type*) [Fintype m] [Fintype n] [Semiring R]
+variable (R : Type*) (m n : Type*) [Fintype m] [Finite n] [Semiring R]
 
 /-- The standard basis of `Matrix m n R`. -/
 noncomputable def stdBasis : Basis (m × n) R (Matrix m n R) :=
@@ -330,8 +331,8 @@ noncomputable def stdBasis : Basis (m × n) R (Matrix m n R) :=
 
 variable {n m}
 
-theorem stdBasis_eq_stdBasisMatrix (i : n) (j : m) [DecidableEq n] [DecidableEq m] :
-    stdBasis R n m (i, j) = stdBasisMatrix i j (1 : R) := by
+theorem stdBasis_eq_stdBasisMatrix (i : m) (j : n) [DecidableEq m] [DecidableEq n] :
+    stdBasis R m n (i, j) = stdBasisMatrix i j (1 : R) := by
   -- Porting note: `simp` fails to apply `Pi.basis_apply`
   ext a b
   by_cases hi : i = a <;> by_cases hj : j = b

@@ -271,7 +271,7 @@ section
 variable (R η)
 
 /-- The basis on `η → R` where the `i`th basis vector is `Function.update 0 i 1`. -/
-noncomputable def basisFun : Basis η R (∀ _ : η, R) :=
+noncomputable def basisFun : Basis η R (η → R) :=
   Basis.ofEquivFun (LinearEquiv.refl _ _)
 #align pi.basis_fun Pi.basisFun
 

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

@@ -98,7 +98,7 @@ theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ
 theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
     ⨆ i ∈ I, range (stdBasis R φ i) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) := by
   refine' iSup_le fun i => iSup_le fun hi => range_le_iff_comap.2 _
-  simp only [←ker_comp, eq_top_iff, SetLike.le_def, mem_ker, comap_iInf, mem_iInf]
+  simp only [← ker_comp, eq_top_iff, SetLike.le_def, mem_ker, comap_iInf, mem_iInf]
   rintro b - j hj
   rw [proj_stdBasis_ne R φ j i, zero_apply]
   rintro rfl

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

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

@@ -182,7 +182,6 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
     exact (hs j).map' _ (ker_stdBasis _ _ _)
   apply linearIndependent_iUnion_finite hs'
   · intro j J _ hiJ
-    simp only
     have h₀ :
       ∀ j, span R (range fun i : ιs j => stdBasis R Ms j (v j i)) ≤
         LinearMap.range (stdBasis R Ms j) := by

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -35,7 +35,7 @@ this is a basis over `Fin 3 → R`.
 -/
 
 
-open Function Submodule
+open Function Set Submodule
 
 open BigOperators
 
@@ -297,6 +297,29 @@ end Module
 
 end Pi
 
+namespace Module
+
+variable (ι R M N : Type*) [Fintype ι] [CommSemiring R]
+  [AddCommMonoid M] [AddCommMonoid N] [Module R M] [Module R N]
+
+/-- The natural linear equivalence: `Mⁱ ≃ Hom(Rⁱ, M)` for an `R`-module `M`. -/
+noncomputable def piEquiv : (ι → M) ≃ₗ[R] ((ι → R) →ₗ[R] M) := Basis.constr (Pi.basisFun R ι) R
+
+lemma piEquiv_apply_apply (v : ι → M) (w : ι → R) :
+    piEquiv ι R M v w = ∑ i, w i • v i := by
+  simp only [piEquiv, Basis.constr_apply_fintype, Basis.equivFun_apply]
+  congr
+
+@[simp] lemma range_piEquiv (v : ι → M) :
+    LinearMap.range (piEquiv ι R M v) = span R (range v) :=
+  Basis.constr_range _ _
+
+@[simp] lemma surjective_piEquiv_apply_iff (v : ι → M) :
+    Surjective (piEquiv ι R M v) ↔ span R (range v) = ⊤ := by
+  rw [← LinearMap.range_eq_top, range_piEquiv]
+
+end Module
+
 namespace Matrix
 
 variable (R : Type*) (m n : Type*) [Fintype m] [Fintype n] [Semiring R]

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

This has nice performance benefits.

@@ -41,7 +41,7 @@ open BigOperators
 
 namespace LinearMap
 
-variable (R : Type _) {ι : Type _} [Semiring R] (φ : ι → Type _) [∀ i, AddCommMonoid (φ i)]
+variable (R : Type*) {ι : Type*} [Semiring R] (φ : ι → Type*) [∀ i, AddCommMonoid (φ i)]
   [∀ i, Module R (φ i)] [DecidableEq ι]
 
 /-- The standard basis of the product of `φ`. -/
@@ -168,11 +168,11 @@ open LinearMap
 
 open Set
 
-variable {R : Type _}
+variable {R : Type*}
 
 section Module
 
-variable {η : Type _} {ιs : η → Type _} {Ms : η → Type _}
+variable {η : Type*} {ιs : η → Type*} {Ms : η → Type*}
 
 theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i, Module R (Ms i)]
     [DecidableEq η] (v : ∀ j, ιs j → Ms j) (hs : ∀ i, LinearIndependent R (v i)) :
@@ -299,7 +299,7 @@ end Pi
 
 namespace Matrix
 
-variable (R : Type _) (m n : Type _) [Fintype m] [Fintype n] [Semiring R]
+variable (R : Type*) (m n : Type*) [Fintype m] [Fintype n] [Semiring R]
 
 /-- The standard basis of `Matrix m n R`. -/
 noncomputable def stdBasis : Basis (m × n) R (Matrix m n R) :=

• 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) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module linear_algebra.std_basis
-! leanprover-community/mathlib commit 13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Matrix.Basis
 import Mathlib.LinearAlgebra.Basis
 import Mathlib.LinearAlgebra.Pi
 
+#align_import linear_algebra.std_basis from "leanprover-community/mathlib"@"13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395"
+
 /-!
 # The standard basis
 

@@ -99,7 +99,7 @@ theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ
 #align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_ne
 
 theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
-    (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) := by
+    ⨆ i ∈ I, range (stdBasis R φ i) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) := by
   refine' iSup_le fun i => iSup_le fun hi => range_le_iff_comap.2 _
   simp only [←ker_comp, eq_top_iff, SetLike.le_def, mem_ker, comap_iInf, mem_iInf]
   rintro b - j hj
@@ -109,7 +109,7 @@ theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
 #align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_proj
 
 theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
-    (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
+    ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
   SetLike.le_def.2
     (by
       intro b hb
@@ -127,14 +127,14 @@ theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu :
 
 theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
-    (⨆ i ∈ I, range (stdBasis R φ i)) = ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) := by
+    ⨆ i ∈ I, range (stdBasis R φ i) = ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) := by
   refine' le_antisymm (iSup_range_stdBasis_le_iInf_ker_proj _ _ _ _ hd) _
   have : Set.univ ⊆ ↑hI.toFinset ∪ J := by rwa [hI.coe_toFinset]
   refine' le_trans (iInf_ker_proj_le_iSup_range_stdBasis R φ this) (iSup_mono fun i => _)
   rw [Set.Finite.mem_toFinset]
 #align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj
 
-theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ := by
+theorem iSup_range_stdBasis [Finite ι] : ⨆ i, range (stdBasis R φ i) = ⊤ := by
   cases nonempty_fintype ι
   convert top_unique (iInf_emptyset.ge.trans <| iInf_ker_proj_le_iSup_range_stdBasis R φ _)
   · rename_i i
@@ -198,7 +198,7 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
       rw [@iSup_singleton _ _ _ fun i => LinearMap.range (stdBasis R (Ms) i)]
       apply h₀
     have h₂ :
-      (⨆ j ∈ J, span R (range fun i : ιs j => stdBasis R Ms j (v j i))) ≤
+      ⨆ j ∈ J, span R (range fun i : ιs j => stdBasis R Ms j (v j i)) ≤
         ⨆ j ∈ J, LinearMap.range (stdBasis R (fun j : η => Ms j) j) :=
       iSup₂_mono fun i _ => h₀ i
     have h₃ : Disjoint (fun i : η => i ∈ ({j} : Set _)) J := by

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -76,7 +76,7 @@ theorem stdBasis_ne (i j : ι) (h : j ≠ i) (b : φ i) : stdBasis R φ i b j =
 #align linear_map.std_basis_ne LinearMap.stdBasis_ne
 
 theorem stdBasis_eq_pi_diag (i : ι) : stdBasis R φ i = pi (diag i) := by
-  ext (x j)
+  ext x j
   -- Porting note: made types explicit
   convert (update_apply (R := R) (φ := φ) (ι := ι) 0 x i j _).symm
   rfl
@@ -314,7 +314,7 @@ variable {n m}
 theorem stdBasis_eq_stdBasisMatrix (i : n) (j : m) [DecidableEq n] [DecidableEq m] :
     stdBasis R n m (i, j) = stdBasisMatrix i j (1 : R) := by
   -- Porting note: `simp` fails to apply `Pi.basis_apply`
-  ext (a b)
+  ext a b
   by_cases hi : i = a <;> by_cases hj : j = b
   · simp [stdBasis, hi, hj, Basis.coe_reindex, comp_apply, Equiv.sigmaEquivProd_symm_apply,
       StdBasisMatrix.apply_same]

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module linear_algebra.std_basis
-! leanprover-community/mathlib commit f8c79b0a623404854a2902b836eac32156fd7712
+! leanprover-community/mathlib commit 13bce9a6b6c44f6b4c91ac1c1d2a816e2533d395
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -289,6 +289,11 @@ theorem basisFun_apply [DecidableEq η] (i) : basisFun R η i = stdBasis R (fun
 theorem basisFun_repr (x : η → R) (i : η) : (Pi.basisFun R η).repr x i = x i := by simp [basisFun]
 #align pi.basis_fun_repr Pi.basisFun_repr
 
+@[simp]
+theorem basisFun_equivFun : (Pi.basisFun R η).equivFun = LinearEquiv.refl _ _ :=
+  Basis.equivFun_ofEquivFun _
+#align pi.basis_fun_equiv_fun Pi.basisFun_equivFun
+
 end
 
 end Module

• leanprover-community/mathlib#19025 (already changed while porting)
• leanprover-community/mathlib#18982

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module linear_algebra.std_basis
-! leanprover-community/mathlib commit f2edd790f6c6e1d660515f76768f63cb717434d7
+! leanprover-community/mathlib commit f8c79b0a623404854a2902b836eac32156fd7712
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -98,22 +98,22 @@ theorem proj_stdBasis_ne (i j : ι) (h : i ≠ j) : (proj i).comp (stdBasis R φ
   LinearMap.ext <| stdBasis_ne R φ _ _ h
 #align linear_map.proj_std_basis_ne LinearMap.proj_stdBasis_ne
 
-theorem supᵢ_range_stdBasis_le_infᵢ_ker_proj (I J : Set ι) (h : Disjoint I J) :
+theorem iSup_range_stdBasis_le_iInf_ker_proj (I J : Set ι) (h : Disjoint I J) :
     (⨆ i ∈ I, range (stdBasis R φ i)) ≤ ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) := by
-  refine' supᵢ_le fun i => supᵢ_le fun hi => range_le_iff_comap.2 _
-  simp only [←ker_comp, eq_top_iff, SetLike.le_def, mem_ker, comap_infᵢ, mem_infᵢ]
+  refine' iSup_le fun i => iSup_le fun hi => range_le_iff_comap.2 _
+  simp only [←ker_comp, eq_top_iff, SetLike.le_def, mem_ker, comap_iInf, mem_iInf]
   rintro b - j hj
   rw [proj_stdBasis_ne R φ j i, zero_apply]
   rintro rfl
   exact h.le_bot ⟨hi, hj⟩
-#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.supᵢ_range_stdBasis_le_infᵢ_ker_proj
+#align linear_map.supr_range_std_basis_le_infi_ker_proj LinearMap.iSup_range_stdBasis_le_iInf_ker_proj
 
-theorem infᵢ_ker_proj_le_supᵢ_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
+theorem iInf_ker_proj_le_iSup_range_stdBasis {I : Finset ι} {J : Set ι} (hu : Set.univ ⊆ ↑I ∪ J) :
     (⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i)) ≤ ⨆ i ∈ I, range (stdBasis R φ i) :=
   SetLike.le_def.2
     (by
       intro b hb
-      simp only [mem_infᵢ, mem_ker, proj_apply] at hb
+      simp only [mem_iInf, mem_ker, proj_apply] at hb
       rw [←
         show (∑ i in I, stdBasis R φ i (b i)) = b by
           ext i
@@ -122,32 +122,32 @@ theorem infᵢ_ker_proj_le_supᵢ_range_stdBasis {I : Finset ι} {J : Set ι} (h
           intro hiI
           rw [stdBasis_same]
           exact hb _ ((hu trivial).resolve_left hiI)]
-      exact sum_mem_bsupᵢ fun i _ => mem_range_self (stdBasis R φ i) (b i))
-#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.infᵢ_ker_proj_le_supᵢ_range_stdBasis
+      exact sum_mem_biSup fun i _ => mem_range_self (stdBasis R φ i) (b i))
+#align linear_map.infi_ker_proj_le_supr_range_std_basis LinearMap.iInf_ker_proj_le_iSup_range_stdBasis
 
-theorem supᵢ_range_stdBasis_eq_infᵢ_ker_proj {I J : Set ι} (hd : Disjoint I J)
+theorem iSup_range_stdBasis_eq_iInf_ker_proj {I J : Set ι} (hd : Disjoint I J)
     (hu : Set.univ ⊆ I ∪ J) (hI : Set.Finite I) :
     (⨆ i ∈ I, range (stdBasis R φ i)) = ⨅ i ∈ J, ker (proj i : (∀ i, φ i) →ₗ[R] φ i) := by
-  refine' le_antisymm (supᵢ_range_stdBasis_le_infᵢ_ker_proj _ _ _ _ hd) _
+  refine' le_antisymm (iSup_range_stdBasis_le_iInf_ker_proj _ _ _ _ hd) _
   have : Set.univ ⊆ ↑hI.toFinset ∪ J := by rwa [hI.coe_toFinset]
-  refine' le_trans (infᵢ_ker_proj_le_supᵢ_range_stdBasis R φ this) (supᵢ_mono fun i => _)
+  refine' le_trans (iInf_ker_proj_le_iSup_range_stdBasis R φ this) (iSup_mono fun i => _)
   rw [Set.Finite.mem_toFinset]
-#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.supᵢ_range_stdBasis_eq_infᵢ_ker_proj
+#align linear_map.supr_range_std_basis_eq_infi_ker_proj LinearMap.iSup_range_stdBasis_eq_iInf_ker_proj
 
-theorem supᵢ_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ := by
+theorem iSup_range_stdBasis [Finite ι] : (⨆ i, range (stdBasis R φ i)) = ⊤ := by
   cases nonempty_fintype ι
-  convert top_unique (infᵢ_emptyset.ge.trans <| infᵢ_ker_proj_le_supᵢ_range_stdBasis R φ _)
+  convert top_unique (iInf_emptyset.ge.trans <| iInf_ker_proj_le_iSup_range_stdBasis R φ _)
   · rename_i i
-    exact ((@supᵢ_pos _ _ _ fun _ => range <| stdBasis R φ i) <| Finset.mem_univ i).symm
+    exact ((@iSup_pos _ _ _ fun _ => range <| stdBasis R φ i) <| Finset.mem_univ i).symm
   · rw [Finset.coe_univ, Set.union_empty]
-#align linear_map.supr_range_std_basis LinearMap.supᵢ_range_stdBasis
+#align linear_map.supr_range_std_basis LinearMap.iSup_range_stdBasis
 
 theorem disjoint_stdBasis_stdBasis (I J : Set ι) (h : Disjoint I J) :
     Disjoint (⨆ i ∈ I, range (stdBasis R φ i)) (⨆ i ∈ J, range (stdBasis R φ i)) := by
   refine'
-    Disjoint.mono (supᵢ_range_stdBasis_le_infᵢ_ker_proj _ _ _ _ <| disjoint_compl_right)
-      (supᵢ_range_stdBasis_le_infᵢ_ker_proj _ _ _ _ <| disjoint_compl_right) _
-  simp only [disjoint_iff_inf_le, SetLike.le_def, mem_infᵢ, mem_inf, mem_ker, mem_bot, proj_apply,
+    Disjoint.mono (iSup_range_stdBasis_le_iInf_ker_proj _ _ _ _ <| disjoint_compl_right)
+      (iSup_range_stdBasis_le_iInf_ker_proj _ _ _ _ <| disjoint_compl_right) _
+  simp only [disjoint_iff_inf_le, SetLike.le_def, mem_iInf, mem_inf, mem_ker, mem_bot, proj_apply,
     funext_iff]
   rintro b ⟨hI, hJ⟩ i
   classical
@@ -183,7 +183,7 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
   have hs' : ∀ j : η, LinearIndependent R fun i : ιs j => stdBasis R Ms j (v j i) := by
     intro j
     exact (hs j).map' _ (ker_stdBasis _ _ _)
-  apply linearIndependent_unionᵢ_finite hs'
+  apply linearIndependent_iUnion_finite hs'
   · intro j J _ hiJ
     simp only
     have h₀ :
@@ -195,12 +195,12 @@ theorem linearIndependent_stdBasis [Ring R] [∀ i, AddCommGroup (Ms i)] [∀ i,
     have h₁ :
       span R (range fun i : ιs j => stdBasis R Ms j (v j i)) ≤
         ⨆ i ∈ ({j} : Set _), LinearMap.range (stdBasis R Ms i) := by
-      rw [@supᵢ_singleton _ _ _ fun i => LinearMap.range (stdBasis R (Ms) i)]
+      rw [@iSup_singleton _ _ _ fun i => LinearMap.range (stdBasis R (Ms) i)]
       apply h₀
     have h₂ :
       (⨆ j ∈ J, span R (range fun i : ιs j => stdBasis R Ms j (v j i))) ≤
         ⨆ j ∈ J, LinearMap.range (stdBasis R (fun j : η => Ms j) j) :=
-      supᵢ₂_mono fun i _ => h₀ i
+      iSup₂_mono fun i _ => h₀ i
     have h₃ : Disjoint (fun i : η => i ∈ ({j} : Set _)) J := by
       convert Set.disjoint_singleton_left.2 hiJ using 0
     exact (disjoint_stdBasis_stdBasis _ _ _ _ h₃).mono h₁ h₂

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>